D. S. McNeil - cp's OEIS frontend

A195264 Iterate x -> A080670(x) (replace x with the concatenation of the primes and exponents in its prime factorization) starting at n until reach 1 or a prime (which is then the value of a(n)); or a(n) = -1 if a prime is never reached.

1, 2, 3, 211, 5, 23, 7, 23, 2213, 2213, 11, 223, 13, 311, 1129, 233, 17, 17137, 19

Offset: 1

N. J. A. Sloane, Sep 14 2011, based on discussions on the Sequence Fans Mailing List by Alonso del Arte, Franklin T. Adams-Watters, D. S. McNeil, Charles R Greathouse IV, Sean A. Irvine, and others

J. H. Conway offered $1000 for a proof or disproof for his conjecture that every number eventually reaches a 1 or a prime - see OEIS50 link. - N. J. A. Sloane, Oct 15 2014
However, James Davis has discovered that a(13532385396179) = -1. This number D = 13532385396179 = (1407*10^5+1)*96179 = 13*53^2*3853*96179 is clearly fixed by the map x -> A080670(x), and so never reaches 1 or a prime. - Hans Havermann, Jun 05 2017
The number n = 3^6 * 2331961591220850480109739369 * 21313644799483579440006455257 is a near-miss for another nonprime fixed point. Unfortunately here the last two factors only look like primes (they have no prime divisors < 10), but in fact both are composite. - Robert Gerbicz, Jun 07 2017
The number D' = 13^532385396179 maps to D and so is a much larger number with a(D') = -1. Repeating this process (by finding a prime prefix of D') should lead to an infinite sequence of counterexamples to Conway's conjecture. - Hans Havermann, Jun 09 2017
The first 47 digits of D' form a prime P = 68971066936841703995076128866117893410448319579, so if Q denotes the remaining digits of 13^532385396179 then D'' = P^Q is another counterexample. - Robert Gerbicz, Jun 10 2017
This sequence is different from A037274. Here 8 = 2^3 -> 23 (a prime), whereas in A037274 8 = 2^3 -> 222 -> ... -> 3331113965338635107 (a prime). - N. J. A. Sloane, Oct 12 2014
The value of a(20) is presently unknown (see A195265).

			4 = 2^2 -> 22 =2*11 -> 211, prime, so a(4) = 211.
9 = 3^2 -> 32 = 2^5 -> 25 = 5^2 -> 52 = 2^2*13 -> 2213, prime, so a(9)=2213.

R. J. Mathar, Table of n, a(n) for n = 1..19
J. H. Conway, Five $1000 Problems, Oct 10 2014 (recorded by Bill Cheswick).
Alonso del Arte and Sean A. Irvine, Table of n, a(n) for n = 1..1000
Hans Havermann, Table of n, a(n) for n = 1..10000 (includes links to lengthy (>40) and unknown-outcome evolutions, and a list of unfactored composites in the unknowns' last step)
Hans Havermann, Table of n, a(n) for n = 1..10000 (includes links to lengthy (>40) and unknown-outcome evolutions, and a list of unfactored composites in the unknowns' last step) [Cached copy, pdf version as of May 08 2018, with permission]
Hans Havermann, 13532385396179 precursors
Hans Havermann, 13532385396179 precursors [Cached copy, pdf version as of May 08 2018, with permission]
OEIS50 DIMACS Conference on Challenges of Identifying Integer Sequences, Problem Session 2, Oct 10 2014, J. H. Conway, Five $1000 Problems (starting at about 06.44). This sequence is mentioned in the fifth problem, starting at around 19:30.
Tony Padilla and Brady Haran, 13532385396179, Numberphile video, 2017
N. J. A. Sloane, Confessions of a Sequence Addict (AofA2017), slides of invited talk given at AofA 2017, Jun 19 2017, Princeton. Mentions this sequence.
N. J. A. Sloane, Three (No, 8) Lovely Problems from the OEIS, Experimental Mathematics Seminar, Rutgers University, Oct 05 2017, Part I, Part 2, Slides. (Mentions this sequence)
Doron Zeilberger, Videos of Talks Delivered in SLOANE75/OEIS50 DIMACS Conference on Challenges of Identifying Integer Sequences (see Problem Session 2, Oct 10 2014)

A variant of the home primes, A037271. Cf. A080670, A195265 (trajectory of 20), A195266 (trajectory of 105), A230305, A084318. A230627 (base-2), A290329 (base-3)

f[1] := 1; f[n_] := Block[{p = Flatten[FactorInteger[n]]}, k = Length[p]; While[k > 0, If[p[[k]] == 1, p = Delete[p, k]]; k--]; FromDigits[Flatten[IntegerDigits[p]]]]; Table[FixedPoint[f, n], {n, 19}] (* Alonso del Arte, based on the program for A080670, Sep 14 2011 *)
fn[n_] := FromDigits[Flatten[IntegerDigits[DeleteCases[Flatten[
FactorInteger[n]], 1]]]];
Table[NestWhile[fn, n, # != 1 && ! PrimeQ[#] &], {n, 19}] (* Robert Price, Mar 15 2020 *)

a(n)={n>1 && while(!ispseudoprime(n), n=A080670(n));n} \\ M. F. Hasler, Oct 12 2014

A186915 T(n,k)=Number of (n+2)X(k+2) 0..6 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.

Original entry on oeis.org

2066505, 59969593, 59969593, 1276581035, 2974946682, 1276581035, 22000126445, 99241308567, 99241308567, 22000126445, 319741716426, 2536761070723, 4813465754996, 2536761070723, 319741716426, 4028133387613, 52666517720011

Offset: 1

R. H. Hardin, general degree formula intuited by D. S. McNeil in the Sequence Fans Mailing List, Feb 28 2011

Table starts
...........2066505.............59969593.............1276581035
..........59969593...........2974946682............99241308567
........1276581035..........99241308567..........4813465754996
.......22000126445........2536761070723........171334955820947
......319741716426.......52666517720011.......4805827783188400
.....4028133387613......921058887545363.....110909004238159456
....44902749582723....13921822487031205....2169936652932512523
...449959668016830...185414592506642580...36804096662464163093
..4103914508092780..2208956268019713255..550615265988952206164
.34409633745323847.23828517723857362267.7367827886026471340866

			Some solutions for 5X4
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..1..1..3..3....1..1..1..5....0..1..4..6....0..1..5..6....1..2..4..4
..1..4..5..5....5..5..5..6....0..3..2..5....1..5..6..0....5..6..0..1

R. H. Hardin, Table of n, a(n) for n = 1..126
R. H. Hardin, Polynomials for columns 1-5

Empirical: T(n,k) is a polynomial of degree 6k+77, for fixed k.
Let T(n,k,z) be the number of (n+2)X(k+2) 0..z arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.
Then empirically T(n,k,z) is a polynomial of degree z*k + z*(z+1)*(z+5)/6 in n, for fixed k.

A186851 Array read by antidiagonals: T(n,k) = number of n-step knight's tours on a (k+2)X(k+2) board summed over all starting positions.

Original entry on oeis.org

9, 16, 16, 25, 48, 16, 36, 96, 104, 16, 49, 160, 328, 208, 16, 64, 240, 664, 976, 400, 16, 81, 336, 1112, 2576, 2800, 800, 16, 100, 448, 1672, 5056, 9328, 8352, 1280, 16, 121, 576, 2344, 8320, 21480, 34448, 21664, 2208, 0, 144, 720, 3128, 12368, 39616, 91328

Offset: 1

R. H. Hardin and D. S. McNeil in the Sequence Fans Mailing List, Feb 27 2011

Here an n-step knight's tour is a directed path with n vertices (or a self-avoiding walk with n-1 steps). - Andrew Howroyd, Jan 02 2023

			Table starts:
   9   16     25      36      49      64      81     100    121    144 ...
  16   48     96     160     240     336     448     576    720    880 ...
  16  104    328     664    1112    1672    2344    3128   4024   5032 ...
  16  208    976    2576    5056    8320   12368   17200  22816  29216 ...
  16  400   2800    9328   21480   39616   63440   92656 127264 167264 ...
  16  800   8352   34448   91328  186544  322528  498320 712080 ...
  16 1280  21664  118480  372384  847520 1584576 2596480 ...
  16 2208  57392  405040 1508784 3846192 7777808 ...
   0 3184 135184 1290112 5807488 ...
   0 4640 317296 4089632 ...
  ...
Some n=3 solutions for 5X5:
  0 0 0 0 0    0 0 0 0 1    0 0 0 0 0    0 0 0 0 0
  0 0 0 0 0    0 0 2 0 0    0 0 0 0 0    0 0 0 0 0
  0 0 1 0 0    0 0 0 0 0    0 0 3 0 0    0 0 0 0 0
  0 0 0 3 0    0 3 0 0 0    2 0 0 0 0    3 0 0 0 1
  0 2 0 0 0    0 0 0 0 0    0 0 1 0 0    0 0 2 0 0

R. H. Hardin, Table of n, a(n) for n = 1..99

Rows 1..8 are A000290(n+2), A035008, A186852, A186853, A186854, A186855, A186856, A186857.
Column 6 is A186441.
Cf. A289204.

\\ G(n) gives polynomial valid for k >= 2*n-4.
Knights={[1,2; 1,-2; -1,2; -1,-2; 2,1; 2,-1; -2,1; -2,-1]}
G(n,f=i->'n-(i-2)) = {
  local(x=vector(n), y=vector(n));
  my(recurse(k)=
     forstep(i=2-k%2, k-1, 2, if(x[i]==x[k] && y[i]==y[k], return(0)));
     if (k==n, f(vecmax(x)-vecmin(x))*f(vecmax(y)-vecmin(y)), sum(i=1, 8, x[k+1] = x[k]+Knights[i,1]; y[k+1]=y[k]+Knights[i,2]; self()(k+1)) );
  );
  if(n==1, recurse(1), x[1]=1; y[1]=2; 8*recurse(2))
}
row(m,n)={my(p=if(n>=2*m-4, G(m,i->'x-(i-2)))); vector(n, k, if(k>=2*m-4, subst(p,'x, k), G(m, i->max(0, k+2-i))))} \\ Andrew Howroyd, Jan 02 2023

Empirical, for all rows: a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3,3,4,6,8,10 respectively for row in 1..6.
From Andrew Howroyd, Jan 02 2023: (Start)
The above empirical formula is correct. Equivalently T(m,n) for given m and n >= 2*m-4 is given by a quadratic polynomial in n. This is because a w X h rectangle can be placed on a k X k grid at integer coordinates in (k-w+1)*(k-h+1) ways when w and h are at most k and every knights path with m vertices spans such a rectangle with width and height at most 2*m - 1.
Sum_{i=2..(k+2)^2} T(i,k)/2 = A289204(k+2).
T(n,k) = 0 for n > (k-2)^2.
(End)

A186180 T(n,k)=Number of (n+2)X(k+2) 0..5 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.

Original entry on oeis.org

520017, 10084236, 10084236, 143369699, 311128593, 143369699, 1662436696, 6520730198, 6520730198, 1662436696, 16382439469, 105970767207, 188034884094, 105970767207, 16382439469, 140871930232, 1414199542732, 4041778238254

Offset: 1

R. H. Hardin, General degree formula intuited by D. S. McNeil in the Sequence Fans Mailing List, Feb 13 2011

Table starts
..........520017..........10084236............143369699............1662436696
........10084236.........311128593...........6520730198..........105970767207
.......143369699........6520730198.........188034884094.........4041778238254
......1662436696......105970767207........4041778238254.......111203560772547
.....16382439469.....1414199542732.......69471558136868......2391923493659465
....140871930232....16059530994398......995828085723859.....42174821764604242
...1078197169699...159099595031390....12251749347425002....629512200937395977
...7459396065112..1400823449171621...132151619698400257...8143852416376007571
..47221234070168.11121210203531892..1270399513311212137..92981285763140685886
.276218909139304.80539662788823416.11027904404610778911.950506396177707075676

			Some solutions for 5X4
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..0..0..0..3....0..0..0..0....0..0..0..0....0..0..0..3....0..0..0..0
..0..0..0..5....0..0..1..2....0..1..1..4....0..1..5..1....0..0..2..3
..0..1..1..0....1..2..0..2....3..1..4..1....5..4..4..5....0..2..5..1

R. H. Hardin, Table of n, a(n) for n = 1..178
R. H. Hardin, Polynomials for columns 1-5

Empirical: T(n,k) is a polynomial of degree 5k+50 in n, for fixed k.
Let T(n,k,z) be the number of (n+2)X(k+2) 0..z arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.
Then empirically T(n,k,z) is a polynomial of degree z*k + z*(z+1)*(z+5)/6 in n, for fixed k.

A186096 T(n,k)=Number of (n+2)X(k+2) 0..4 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.

Original entry on oeis.org

102251, 1252889, 1252889, 11258613, 22559052, 11258613, 83378583, 280102672, 280102672, 83378583, 531218757, 2743553694, 4527262140, 2743553694, 531218757, 2985984444, 22408644868, 55707179395, 55707179395, 22408644868, 2985984444

Offset: 1

R. H. Hardin, General degree formula intuited by D. S. McNeil in the Sequence Fans Mailing List, Feb 12 2011

Table starts
........102251.........1252889.........11258613...........83378583
.......1252889........22559052........280102672.........2743553694
......11258613.......280102672.......4527262140........55707179395
......83378583......2743553694......55707179395.......837192826927
.....531218757.....22408644868.....558643720724.....10064164793382
....2985984444....157927508610....4754203179765....101247852066065
...15084070635....983600385660...35285910378578....878623899164100
...69482992431...5510351270895..232998389350277...6723402580436327
..295278398390..28148281162513.1389861134920751..46135247077059665
.1168636004931.132536596243411.7581135805604097.287649593317228144

			Some solutions for 5X4
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..0..0..0..2....0..0..0..2....0..0..0..2....0..0..1..2....0..0..1..2
..0..1..2..1....1..1..2..2....1..1..2..0....1..2..4..4....0..2..1..2
..2..3..3..4....1..2..0..0....3..4..0..1....1..4..1..3....2..4..3..2

R. H. Hardin, Table of n, a(n) for n = 1..219
R. H. Hardin, Polynomials for columns 1-8

Empirical: T(n,k) is a polynomial of degree 4k+30 in n, for fixed k.
Let T(n,k,z) be the number of (n+2)X(k+2) 0..z arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.
Then empirically T(n,k,z) is a polynomial of degree z*k + z*(z+1)*(z+5)/6 in n, for fixed k.

A185477 T(n,k)=Number of (n+2)X(k+2) 0..2 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.

Original entry on oeis.org

1169, 4594, 4594, 13659, 21834, 13659, 34779, 76309, 76309, 34779, 79743, 225672, 308692, 225672, 79743, 169052, 594798, 1043186, 1043186, 594798, 169052, 336690, 1433903, 3097348, 3959167, 3097348, 1433903, 336690, 636698, 3212372, 8297059

Offset: 1

R. H. Hardin, General degree formula intuited by D. S. McNeil in the Sequence Fans Mailing List, Jan 28 2011

Table starts
....1169.....4594.....13659......34779......79743......169052.......336690
....4594....21834.....76309.....225672.....594798.....1433903......3212372
...13659....76309....308692....1043186....3097348.....8297059.....20411234
...34779...225672...1043186....3959167...12990375....37961900....100908633
...79743...594798...3097348...12990375...46410729...146203201....416227164
..169052..1433903...8297059...37961900..146203201...493061605...1497314456
..336690..3212372..20411234..100908633..416227164..1497314456...4845252741
..636698..6763143..46732687..247920339.1090826214..4179700035..14425457557
.1151966.13496424.100636591..570069808.2669230399.10893560939..40183952539
.2005704.25706057.205574323.1239033996.6166331968.26828743607.106069534256

			Some solutions for 5X4
..0..0..0..0....0..0..1..1....0..0..0..1....0..0..0..2....0..0..0..1
..0..0..0..2....1..1..1..2....0..0..0..1....1..1..1..2....0..0..1..2
..0..0..1..2....1..1..1..2....0..0..0..1....1..1..1..2....0..1..2..2
..0..1..1..2....1..1..2..1....1..1..2..1....1..1..1..2....0..2..0..0
..2..1..1..2....1..2..0..2....2..2..1..0....1..1..2..2....0..2..2..2

R. H. Hardin, Table of n, a(n) for n = 1..1404
R. H. Hardin, Polynomials for columns 1-8

Empirical: T(n,k) is a polynomial of degree 2k+7 in n, for fixed k.
Let T(n,k,z) be the number of (n+2)X(k+2) 0..z arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.
Then empirically T(n,k,z) is a polynomial of degree z*k + z*(z+1)*(z+5)/6 in n, for fixed k.

A185435 T(n,k)=Number of (n+2)X(k+2) 0..7 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.

Original entry on oeis.org

6842284, 284037544, 284037544, 8653394212, 21536560306, 8653394212, 212298419684, 1090205284029, 1090205284029, 212298419684, 4370405405266, 41910604337378, 84722449466168, 41910604337378, 4370405405266

Offset: 1

R. H. Hardin, General degree formula intuited by D. S. McNeil in the Sequence Fans Mailing List, Jan 27 2011

Table starts
.............6842284..............284037544................8653394212
...........284037544............21536560306.............1090205284029
..........8653394212..........1090205284029............84722449466168
........212298419684.........41910604337378..........4772160687307074
.......4370405405266.......1297535366114472........209290512833668811
......77657199293322......33575010264022917.......7468756070356586903
....1216284173329482.....745543958045415621.....223694029250999654095
...17062128865116751...14492443009379677098....5755145891541173071730
..217083576402029968..250496452202647761530..129520045203909930078682
.2530473438240068012.3898612401674733619729.2587203198419699686906895

			Some solutions for 5X4
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..0..0..0..0....0..0..0..4....0..0..0..0....0..0..0..0....0..0..0..4
..0..1..1..2....0..0..2..3....0..1..4..5....0..0..5..6....0..0..6..7
..0..3..7..3....0..7..0..5....0..2..1..6....2..2..6..4....0..4..3..0

R. H. Hardin, Table of n, a(n) for n = 1..83
R. H. Hardin, Polynomials for columns 1-3

Empirical: T(n,k) is a polynomial of degree 7k+112, for fixed k
Let T(n,k,z) be the number of (n+2)X(k+2) 0..z arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order
Then empirically T(n,k,z) is a polynomial of degree z*k + z*(z+1)*(z+5)/6 in n, for fixed k.

A184574 T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.

Original entry on oeis.org

14178, 102445, 102445, 545662, 993538, 545662, 2430950, 6803631, 6803631, 2430950, 9496395, 37767705, 57374460, 37767705, 9496395, 33351260, 179122657, 380532059, 380532059, 179122657, 33351260, 107058241, 748499580, 2113138210

Offset: 1

R. H. Hardin, general degree formula intuited by D. S. McNeil in the Sequence Fans Mailing List, Jan 17 2011

Table starts
......14178......102445........545662........2430950.........9496395
.....102445......993538.......6803631.......37767705.......179122657
.....545662.....6803631......57374460......380532059......2113138210
....2430950....37767705.....380532059.....2943827443.....18803004899
....9496395...179122657....2113138210....18803004899....136680720320
...33351260...748499580...10202200416...103444456133....848542379467
..107058241..2816118529...43935544294...503785839330...4626643143791
..318063303..9696377100..171891306894..2213469458762..22587829272879
..883398416.30941723282..619309263773..8896632071640.100176548344077
.2312834051.92420016377.2076328840978.33064363109286.408222405584237

			Some solutions for 5X4
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..0..0..1..1....0..0..0..1....0..0..1..1....0..0..0..0....0..0..0..0
..0..0..1..2....0..0..1..1....0..0..1..1....0..0..0..2....0..0..1..2
..2..3..0..0....0..0..3..3....0..3..1..3....1..2..2..2....0..2..3..2
..2..3..0..1....0..1..2..2....1..3..3..3....3..2..3..0....0..3..3..1

R. H. Hardin, Table of n, a(n) for n = 1..480
R. H. Hardin, Polynomials for columns 1-8

Empirical: T(n,k) is a polynomial of degree 3k+16 in n, for fixed k.
Let T(n,k,z) be the number of (n+2)X(k+2) 0..z arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.
Then empirically T(n,k,z) is a polynomial of degree z*k + z*(z+1)*(z+5)/6 in n, for fixed k.

A184548 T(n,k)=Number of (n+2)X(k+2) binary arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.

Original entry on oeis.org

45, 89, 89, 147, 193, 147, 220, 340, 340, 220, 309, 537, 631, 537, 309, 415, 792, 1048, 1048, 792, 415, 539, 1114, 1627, 1837, 1627, 1114, 539, 682, 1513, 2413, 3024, 3024, 2413, 1513, 682, 845, 2000, 3461, 4774, 5313, 4774, 3461, 2000, 845, 1029, 2587, 4837

Offset: 1

R. H. Hardin, general degree formula intuited by D. S. McNeil in the Sequence Fans Mailing List, Jan 16 2011

Table starts
...45...89..147...220...309....415....539....682.....845....1029....1235
...89..193..340...537...792...1114...1513...2000....2587....3287....4114
..147..340..631..1048..1627...2413...3461...4837....6619....8898...11779
..220..537.1048..1837..3024...4774...7307..10909...15944...22867...32238
..309..792.1627..3024..5313...8989..14767..23648...36997...56634...84939
..415.1114.2413..4774..8989..16345..28844..49489...82648..134509..213640
..539.1513.3461..7307.14767..28844..54543..99872..177207..305112..510719
..682.2000.4837.10909.23648..49489..99872.194245..364432..660821.1160932
..845.2587.6619.15944.36997..82648.177207.364432..719905.1369596.2516995
.1029.3287.8898.22867.56634.134509.305112.660821.1369596.2725367.5225554

			Some solutions for 5X4
..0..0..0..1....0..0..0..1....0..0..0..0....0..0..0..1....0..0..0..0
..0..0..1..1....0..0..0..1....0..0..0..0....0..0..1..1....0..0..0..0
..0..0..1..1....0..0..1..1....0..0..0..0....0..0..1..1....0..0..0..0
..0..1..0..0....0..1..0..1....0..0..0..1....0..1..1..1....0..0..1..1
..1..1..0..0....1..1..0..1....1..1..1..0....0..1..1..1....1..1..0..1

R. H. Hardin, Table of n, a(n) for n = 1..9378
R. H. Hardin, Polynomials for columns 1-8

Empirical: T(n,k) is a polynomial of degree k+2 in n, for fixed k.
Let T(n,k,z) be the number of (n+2)X(k+2) 0..z arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.
Then empirically T(n,k,z) is a polynomial of degree z*k + z*(z+1)*(z+5)/6 in n, for fixed k.

A180388 Number of permutations of 1..n with number of rises (p(i+1)>p(i)) different from number of rises in the inverse permutation.

Original entry on oeis.org

0, 0, 0, 0, 2, 24, 228, 2088, 19732, 197890, 2131060, 24729108, 309027560, 4148115048, 59611031304, 913915160628, 14897443573244, 257369478424890, 4698494631208500, 90393611677083892, 1828153614233855024, 38778554791649355232, 860921156414834534368

Offset: 0

Leroy Quet, D. S. McNeil and R. H. Hardin in the Sequence Fans Mailing List Sep 01 2010

nonn

Vaclav Kotesovec, Table of n, a(n) for n = 0..200

a(n) + A180389(n) = n! = A000142(n).

More terms from Vaclav Kotesovec, Jun 10 2015

a(0)=0 prepended by Alois P. Heinz, Jun 10 2015

cp's OEIS Frontend

User: D. S. McNeil

A195264 Iterate x -> A080670(x) (replace x with the concatenation of the primes and exponents in its prime factorization) starting at n until reach 1 or a prime (which is then the value of a(n)); or a(n) = -1 if a prime is never reached.

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A186915 T(n,k)=Number of (n+2)X(k+2) 0..6 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.

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A186851 Array read by antidiagonals: T(n,k) = number of n-step knight's tours on a (k+2)X(k+2) board summed over all starting positions.

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A186180 T(n,k)=Number of (n+2)X(k+2) 0..5 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.

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A186096 T(n,k)=Number of (n+2)X(k+2) 0..4 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.

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A185477 T(n,k)=Number of (n+2)X(k+2) 0..2 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.

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A185435 T(n,k)=Number of (n+2)X(k+2) 0..7 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.

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A184574 T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.

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A184548 T(n,k)=Number of (n+2)X(k+2) binary arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.

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