A052919 -id:A052919 - cp's OEIS frontend

A008776 Pisot sequences E(2,6), L(2,6), P(2,6), T(2,6).

2, 6, 18, 54, 162, 486, 1458, 4374, 13122, 39366, 118098, 354294, 1062882, 3188646, 9565938, 28697814, 86093442, 258280326, 774840978, 2324522934, 6973568802, 20920706406, 62762119218, 188286357654, 564859072962, 1694577218886, 5083731656658, 15251194969974

Offset: 0

N. J. A. Sloane, David W. Wilson

Definitions of Pisot and related sequences:
Pisot sequence E(x, y): a(0) = x, a(1) = y, a(n) = floor(a(n-1)^2/a(n-2) + 1/2) = nearest integer to a(n-1)^2/a(n-2), with 0 < x < y.
Pisot sequence L(x, y): a(0) = x, a(1) = y, a(n) = ceiling(a(n-1)^2/a(n-2)).
Pisot sequence P(x, y): a(0) = x, a(1) = y, a(n) = ceiling(a(n-1)^2/a(n-2) - 1/2).
Pisot sequence T(x, y): a(0) = x, a(1) = y, a(n) = floor(a(n-1)^2/a(n-2)).
Pisot/Shallit sequence S(x, y): a(0) = x, a(1) = y, a(n) = floor(a(n-1)^2/a(n-2)+1).
A025192 is the main entry for the sequence of numbers 2*3^n.
Number of tilings of a 4 X (4n+4) rectangle into T tetrominoes.
Numbers n such that 3^n = n/2 mod n. Cf. A066601 3^n mod n. - Zak Seidov, Aug 26 2006, Nov 20 2008
For n >= 1, a(n) is equal to the number of functions f:{1,2...,n}->{1,2,3} such that for a fixed x in {1,2,...,n} and a fixed y in {1,2,3} we have f(x) != y. - Aleksandar M. Janjic and Milan Janjic, Mar 27 2007
a(n+1) is the number of compositions of n when there are 2 types of each natural number. - Milan Janjic, Aug 13 2010
2*Sum_{n>=2} 1/A083667(n) = 2*Sum_{n>=2} 2^(-n)*3^(-((n*(n-1))/2)) = Sum_{n>=1} 1/Product_{k=1..n} A008776(k) = Sum_{n>=1} 1/Product_{k=1..n} 2*3^k = 0.17609845431233461692099660022134... . - Alexander R. Povolotsky, Aug 08 2011
Number of monic squarefree polynomials over F_3 of degree n+1. - Charles R Greathouse IV, Feb 07 2012
a(n) is the sum of the elements of the n-th power of the matrix {{1, 2}, {2, 1}}. - Griffin N. Macris, Mar 25 2016
Let D(m) denote the set of divisors of a number m, and consider s1(m) and s2(m) the sums of those divisors that are congruent to 1 and 2 (mod 3) respectively. This sequence lists the numbers m such that s1(m) = 1 and s2(m) = 2. - Michel Lagneau, Feb 09 2017
a(n) is the multiplicative order of k modulo 3^(n+1), where k is any number congruent to 2 or 5 modulo 9. Note that for n > 0, k is a primitive root modulo 3^(n+1) if and only if k == 2, 5 (mod 9). - Jianing Song, Apr 20 2021

S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see p. 203).

Franklin T. Adams-Watters, Table of n, a(n) for n = 0..200
Shaoshi Chen, Hanqian Fang, Sergey Kitaev, and Candice X.T. Zhang, Patterns in Multi-dimensional Permutations, arXiv:2411.02897 [math.CO], 2024. See pp. 2, 26.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 170
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
Tanya Khovanova, Recursive Sequences
Craig Knecht, Sphinx tiling of a repetitive shape.
C. Moore, Some Polyomino Tilings of the Plane, arXiv:math/9905012 [math.CO], 1999.
C. Pisot, La répartition modulo 1 et les nombres algébriques, Ann. Scu. Norm. Sup. Pisa 2 ser, vol 7. no 3-4 (1938) p 205-248.
Index entries for linear recurrences with constant coefficients, signature (3).

Apart from initial term, same as A025192.
Cf. A080643.
Cf. A000244.

List([0..30], n-> 2*3^n); # G. C. Greubel, Sep 11 2019

a008776 = (* 2) . (3 ^)
a008776_list = iterate (* 3) 2  -- Reinhard Zumkeller, Oct 19 2015

[2*3^n: n in [0..30]]; // G. C. Greubel, Sep 11 2019

# E(x,y) is f(n,x,y,1/2), T(x,y) is f(n,x,y,0), and S(x,y) is f(n,x,y,1).
f:=proc(n,x,y,r) option remember;
if n=0 then x
elif n=1 then y
else floor(f(n-1,x,y,r)^2/f(n-2,x,y,r) + r); fi; end;
[seq(f(n,2,6,1/2),n=0..30)];
# N. J. A. Sloane, Jul 30 2016

Table[EulerPhi[3^n], {n, 0, 100}] (* Artur Jasinski, Nov 19 2008 *)
Table[MatrixPower[{{1,2},{1,2}},n][[1]][[2]],{n,0,44}] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2010 *)
NestList[3#&,2,50] (* Harvey P. Dale, Nov 28 2022 *)

a(n)=3^n<<1 \\ corrected by Michel Marcus, Aug 03 2015

def A008776(n): return 3**n<<1 # Chai Wah Wu, Apr 02 2025

[2*3^n for n in (0..30)] # G. C. Greubel, Sep 11 2019

a(n) = 2*3^n.
a(n) = 3*a(n-1).
G.f.: 2/(1-3*x). - Philippe Deléham, Oct 08 2007
a(n-1) = phi(3^n). - Artur Jasinski, Nov 19 2008
E.g.f.: 2*exp(3*x). - Mohammad K. Azarian, Jan 15 2009
From Paul Curtz, Jan 20 2009: (Start)
a(n) = A048473(n) + 1.
a(n) = A052919(n+1)-1.
a(n) = A115099(n) - 2.
a(n) = A100774(n) + 2. (End)
If p[i]=2, (i >= 1), and if A is Hessenberg matrix of order n defined by: A[i,j] = p[j-i+1], (i <= j), A[i,j]=-1, (i=j+1), and A[i,j]=0 otherwise. Then, for n >= 1, a(n-1)=det A. - Milan Janjic, Apr 29 2010
G.f.: ((1/2)/G(0)-1)/x^2 where G(k) = 1 - 2^k/(2 - 4*x/(2*x - 2^k/G(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Dec 22 2012
G.f.: -G(0)/x where G(k) = 1 - 1/(1-2*x)/(1-x/(x-1/G(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Jan 25 2013
G.f.: (1 - 1/Q(0))/x where Q(k) = 1 - x*(2*k-2)/(1 - x*(2*k+5)/Q(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Mar 19 2013
G.f.: W(0), where W(k) = 1 + 1/(1 - x*(2*k+3)/(x*(2*k+4) + 1/W(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Aug 28 2013

Jasinski formula corrected by Charles R Greathouse IV, Feb 18 2011

A111974 Primes of the form 2*3^k + 1.

Original entry on oeis.org

3, 7, 19, 163, 487, 1459, 39367, 86093443, 258280327, 411782264189299, 116299474006080119380780339, 3140085798164163223281069127, 84782316550432407028588866403, 20602102921755074907947094535687, 1910009901593650473786381403548828023839870277948686259673707683

Offset: 1

T. D. Noe, Aug 24 2005

nonn

Amiram Eldar, Table of n, a(n) for n = 1..23
Hartosh Singh Bal and Gaurav Bhatnagar, Prime number conjectures from the Shapiro class structure, arXiv:1903.09619 [math.NT], 2019-2020.

Cf. A003306 (k such that 2*3^k + 1 is prime), A003307 (k such that 2*3^k - 1 is prime), A052919.

Mathematica
```
Select[2*3^Range[100]+1, PrimeQ]
```

a(n) = A052919(A003306(n)+1). - Amiram Eldar, Jul 18 2025

a(15) from Amiram Eldar, Jul 18 2025

A237930 a(n) = 3^(n+1) + (3^n-1)/2.

Original entry on oeis.org

3, 10, 31, 94, 283, 850, 2551, 7654, 22963, 68890, 206671, 620014, 1860043, 5580130, 16740391, 50221174, 150663523, 451990570, 1355971711, 4067915134, 12203745403, 36611236210, 109833708631, 329501125894, 988503377683, 2965510133050, 8896530399151

Offset: 0

Philippe Deléham, Feb 16 2014

a(n-1) agrees with the graph radius of the n-Sierpinski carpet graph for n = 2 to at least n = 5. See A100774 for the graph diameter of the n-Sierpinski carpet graph.
The inverse binomial transform gives 3, 7, 14, 28, 56, ... i.e., A005009 with a leading 3. - R. J. Mathar, Jan 08 2020
First differences of A108765. The digital root of a(n) for n > 1 is always 4. a(n) is never divisible by 7 or by 12. a(n) == 10 (mod 84) for odd n. a(n) == 31 (mod 84) for even n > 0. Conjecture: This sequence contains no prime factors p == {11, 13, 23, 61 71, 73} (mod 84). - Klaus Purath, Apr 13 2020
This is a subsequence of A017209 for n > 1. See formula. - Klaus Purath, Jul 03 2020

			Ternary....................Decimal
10...............................3
101.............................10
1011............................31
10111...........................94
101111.........................283
1011111........................850
10111111......................2551
101111111.....................7654, etc.

Colin Barker, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Graph Radius.
Eric Weisstein's World of Mathematics, Sierpinski Carpet Graph.
Index entries for linear recurrences with constant coefficients, signature (4,-3).

Cf. A000244, A003462, A005009, A005032 (first differences), A017209, A060816, A100774, A108765 (partial sums), A199109, A329774.

Cf. A024023, A029858, A057198, A116952, A171498.

[3^(n+1) + (3^n-1)/2: n in [0..40]]; // Vincenzo Librandi, Jan 09 2020

(* Start from Eric W. Weisstein, Mar 13 2018 *)
Table[(7 3^n - 1)/2, {n, 0, 20}]
(7 3^Range[0, 20] - 1)/2
LinearRecurrence[{4, -3}, {10, 31}, {0, 20}]
CoefficientList[Series[(3 - 2 x)/((x - 1) (3 x - 1)), {x, 0, 20}], x]
(* End *)

Vec((3 - 2*x) / ((1 - x)*(1 - 3*x)) + O(x^30)) \\ Colin Barker, Nov 27 2019

G.f.: (3-2*x)/((1-x)*(1-3*x)).
a(n) = A000244(n+1) + A003462(n).
a(n) = 3*a(n-1) + 1 for n > 0, a(0)=3. (Note that if a(0) were 1 in this recurrence we would get A003462, if it were 2 we would get A060816. - N. J. A. Sloane, Dec 06 2019)
a(n) = 4*a(n-1) - 3*a(n-2) for n > 1, a(0)=3, a(1)=10.
a(n) = 2*a(n-1) + 3*a(n-2) + 2 for n > 1.
a(n) = A199109(n) - 1.
a(n) = (7*3^n - 1)/2. - Eric W. Weisstein, Mar 13 2018
From Klaus Purath, Apr 13 2020: (Start)
a(n) = A057198(n+1) + A024023(n).
a(n) = A029858(n+2) - A024023(n).
a(n) = A052919(n+1) + A029858(n+1).
a(n) = (A000244(n+1) + A171498(n))/2.
a(n) = 7*A003462(n) + 3.
a(n) = A116952(n) + 2. (End)
a(n) = A017209(7*(3^(n-2)-1)/2 + 3), n > 1. - Klaus Purath, Jul 03 2020
E.g.f.: exp(x)*(7*exp(2*x) - 1)/2. - Stefano Spezia, Aug 28 2023

A100702 Number of layers of dough separated by butter in successive foldings of croissant dough.

Original entry on oeis.org

1, 3, 7, 19, 55, 163, 487, 1459, 4375, 13123, 39367, 118099, 354295, 1062883, 3188647, 9565939, 28697815, 86093443, 258280327, 774840979, 2324522935, 6973568803, 20920706407, 62762119219, 188286357655, 564859072963

Offset: 0

Daniel Wolf (djwolf1(AT)axelero.hu), Dec 09 2004

At each trebling of layers following the first, two sets of layers, not separated from their neighbors by butter, are combined. Traditional patisserie stops at 55 layers, but forgetful chefs have been known to make additional folds to 163 layers.
This sequence also describes the number of moves of the k-th disk solving (non-optimally) the [RED ; NEUTRAL ; NEUTRAL] or [NEUTRAL ; NEUTRAL ; BLUE] pre-colored Magnetic Tower of Hanoi puzzle (see the "CROSSREFS" in A183120). For other Magnetic Tower of Hanoi related sequences cf. A183111-A183125.
Same as A052919 except first term is 1, not 2. - Omar E. Pol, Feb 20 2011

J. Child and M. Beck, Mastering the Art of French Cooking, Vol. 2

Uri Levy, The Magnetic Tower of Hanoi, arXiv:1003.0225 [math.CO], 2010.
Index entries for linear recurrences with constant coefficients, signature (4, -3).

Cf. A052919.

Join[{1}, LinearRecurrence[{4, -3}, {3, 7}, 25]] (* Jean-François Alcover, Jul 28 2018 *)

a(n)=([0,1; -3,4]^n*[1;3])[1,1] \\ Charles R Greathouse IV, Jan 28 2018

For n > 1, a(n) = 3*a(n-1) - 2.
From R. J. Mathar, Jun 30 2009: (Start)
a(n) = 1 + 2*3^(n-1), n > 0.
a(n) = 4*a(n-1) - 3*a(n-2), n > 2.
G.f.: -(1+x)*(2*x-1)/((3*x-1)*(x-1)). (End)

A176040 Periodic sequence: Repeat 3, 1.

Original entry on oeis.org

3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3

Offset: 0

Klaus Brockhaus, Apr 07 2010

Interleaving of A010701 and A000012.
Also continued fraction expansion of (3+sqrt(21))/2.
Also decimal expansion of 31/99.
Essentially first differences of A014601.
Inverse binomial transform of 3 followed by A020707.
Second inverse binomial transform of A052919 without initial term 2.
Third inverse binomial transform of A007582 without initial term 1.
Exp( Sum_{n >= 1} a(n)*x^n/n ) = 1 + x + 2*x^2 + 2*x^3 + 3*x^4 + 3*x^5 + ... is the o.g.f. for A008619. - Peter Bala, Mar 13 2015

Index entries for linear recurrences with constant coefficients, signature (0,1).

Cf. A153284, A010701 (all 3's sequence), A000012 (all 1's sequence), A090458 (decimal expansion of (3+sqrt(21))/2), A010684 (repeat 1, 3), A014601 (congruent to 0 or 3 mod 4), A020707 (2^(n+2)), A052919, A007582 (2^(n-1)*(1+2^n)), A008619.

&cat[ [3, 1]: n in [0..52] ];
[ 2+(-1)^n: n in [0..104] ];

PadRight[{},120,{3,1}] (* or *) LinearRecurrence[{0,1},{3,1},120] (* Harvey P. Dale, Mar 11 2015 *)

a(n) = 2+(-1)^n.
a(n) = a(n-2) for n > 1; a(0) = 3, a(1) = 1.
a(n) = -a(n-1)+4 for n > 0; a(0) = 3.
a(n) = 3*((n+1) mod 2)+(n mod 2).
a(n) = A010684(n+1).
G.f.: (3+x)/((1-x)*(1+x)).
From Amiram Eldar, Jan 01 2023: (Start)
Multiplicative with a(2^e) = 3, and a(p^e) = 1 for p >= 3.
Dirichlet g.f.: zeta(s)*(1+2^(1-s)). (End)

A222838 T(n,k)=Number of nXk 0..3 arrays with no element equal to another at a city block distance of exactly two, and new values 0..3 introduced in row major order.

Original entry on oeis.org

1, 2, 2, 3, 7, 3, 7, 24, 24, 7, 19, 96, 72, 96, 19, 55, 384, 216, 216, 384, 55, 163, 1536, 648, 600, 648, 1536, 163, 487, 6144, 1944, 1536, 1536, 1944, 6144, 487, 1459, 24576, 5832, 4056, 4032, 4056, 5832, 24576, 1459, 4375, 98304, 17496, 10584, 9600, 9600, 10584

Offset: 1

R. H. Hardin Mar 06 2013

Table starts
.....1.......2.......3.......7......19......55.....163......487.....1459
.....2.......7......24......96.....384....1536....6144....24576....98304
.....3......24......72.....216.....648....1944....5832....17496....52488
.....7......96.....216.....600....1536....4056...10584....27744....72600
....19.....384.....648....1536....4032....9600...22848....55296...133824
....55....1536....1944....4056....9600...24576...55296...124416...279936
...163....6144....5832...10584...22848...55296..138240...301056...642048
...487...24576...17496...27744...55296..124416..301056...743424..1572864
..1459...98304...52488...72600..133824..279936..642048..1572864..3833856
..4375..393216..157464..190104..322944..645504.1382400..3250176..7962624
.13123.1572864..472392..497664..779328.1476096.3022848..6690816.15925248
.39367.6291456.1417176.1302936.1881600.3393024.6690816.14155776.31850496

			Some solutions for n=4 k=4
..0..0..1..2....0..1..2..3....0..0..1..2....0..0..1..2....0..1..1..2
..2..2..1..0....2..3..0..0....1..3..3..0....2..3..3..2....2..2..0..3
..1..3..3..0....2..3..1..1....1..2..2..0....1..1..0..0....1..3..0..1
..1..0..2..2....1..0..2..2....0..0..1..3....0..2..2..3....0..3..2..2

R. H. Hardin, Table of n, a(n) for n = 1..312

Column 1 is A052919(n-2)

Empirical for column k:
k=1: a(n) = 4*a(n-1) -3*a(n-2) for n>4
k=2: a(n) = 4*a(n-1) for n>3
k=3: a(n) = 3*a(n-1) for n>2
k=4: a(n) = 2*a(n-1) +2*a(n-2) -a(n-3) for n>4
k=5: a(n) = 2*a(n-1) +2*a(n-3) +a(n-4) for n>7
k=6: a(n) = 2*a(n-1) +2*a(n-2) -4*a(n-3) +4*a(n-4) -4*a(n-5) +2*a(n-6) -6*a(n-7) +a(n-10) for n>14
k=7: a(n) = 2*a(n-1) +a(n-3) -2*a(n-4) +4*a(n-5) +a(n-6) -a(n-9) for n>14

A094617 Triangular array T of numbers generated by these rules: 2 is in T; and if x is in T, then 2x-1 and 3x-2 are in T.

Original entry on oeis.org

2, 3, 4, 5, 7, 10, 9, 13, 19, 28, 17, 25, 37, 55, 82, 33, 49, 73, 109, 163, 244, 65, 97, 145, 217, 325, 487, 730, 129, 193, 289, 433, 649, 973, 1459, 2188, 257, 385, 577, 865, 1297, 1945, 2917, 4375, 6562, 513, 769, 1153, 1729, 2593, 3889, 5833, 8749, 13123, 19684

Offset: 1

Clark Kimberling, May 14 2004

To obtain row n from row n-1, apply 2x-1 to each x in row n-1 and then put 1+3^n at the end. Or, instead, apply 3x-2 to each x in row n-1 and then put 1+2^n at the beginning.
From Lamine Ngom, Feb 10 2021: (Start)
Triangle read by diagonals provides all the sequences of the form 1+2^(k-1)*3^n, where k is the k-th diagonal.
For instance, the terms of the first diagonal form the sequence 2, 4, 10, 28, ..., i.e., 1+3^n (A034472).
The 2nd diagonal leads to the sequence 3, 7, 19, 55, ..., i.e., 1+2*3^n (A052919).
The 3rd diagonal is the sequence 5, 13, 37, 109, ..., i.e., 1+4*3^n (A199108).
And for k = 4, we obtain the sequence 9, 25, 73, 217, ..., i.e., 1+8*3^n (A199111). (End)

			Rows of this triangle begin:
    2;
    3,   4;
    5,   7,   10;
    9,  13,   19,   28;
   17,  25,   37,   55,   82;
   33,  49,   73,  109,  163,  244;
   65,  97,  145,  217,  325,  487,  730;
  129, 193,  289,  433,  649,  973, 1459, 2188;
  257, 385,  577,  865, 1297, 1945, 2917, 4375,  6562;
  513, 769, 1153, 1729, 2593, 3889, 5833, 8749, 13123, 19684;
  ...

Ivan Neretin, Table of n, a(n) for n = 1..5151

Cf. A094616, A094618, A138247.

Cf. A034472, A052919, A199108, A199111.

FoldList[Append[2 #1 - 1, 1 + 3^#2] &, {2}, Range[9]] // Flatten (* Ivan Neretin, Mar 30 2016 *)

When offset is zero, then the first term is T(0,0) = 2, and
T(n,0) = 1 + 2^n = A000051(n),
T(n,n) = 1 + 3^n = A048473(n),
T(2n,n) = 1 + 6^n = A062394(n).
Row sums = A094618.
a(n) = A036561(n-1) + 1. - Filip Zaludek, Nov 19 2016

A062547 a(n) is least odd integer not a partial sum of 1, 3, ..., a(n-1).

Original entry on oeis.org

1, 3, 5, 7, 17, 19, 53, 55, 161, 163, 485, 487, 1457, 1459, 4373, 4375, 13121, 13123, 39365, 39367, 118097, 118099, 354293, 354295, 1062881, 1062883, 3188645, 3188647, 9565937, 9565939, 28697813, 28697815, 86093441, 86093443, 258280325, 258280327, 774840977

Offset: 0

Wouter Meeussen, Jun 26 2001

			Partial sums of 1;3;5 are 1;3;4;5;6;8;9 and 7 is the least missing odd integer, hence the next term is 7.

Index entries for linear recurrences with constant coefficients, signature (-1,3,3).

Cf. A048473, A052919, A062548.

Table[ -1+ 2 3^Floor[k/2]+2 Mod[k, 2], {k, 0, 36}]
LinearRecurrence[{-1,3,3},{1,3,5},40] (* Harvey P. Dale, Jul 14 2018 *)

a(2*n) = A048473(n); a(2n+1) = a(2n)+2.
For n > 0, a(2*n) = 3*a(2*n-1) - 4; a(2*n+1) = a(2*n) + 2 = A052919(n+1).
From Bruno Berselli, Jan 28 2011: (Start)
G.f.: (1+4*x+5*x^2)/((1+x)*(1-3*x^2)).
a(n) = -a(n-1) + 3*a(n-2) + 3*a(n-3) for n > 2.
a(n) = 2*3^((2*n + (-1)^n - 1)/4) - (-1)^n. (End)

Edited by Michel Marcus, Mar 16 2024

A182949 Joint-rank array of the numbers (3i+1)3^j, where i>=0, j>=0, by antidiagonals.

Original entry on oeis.org

1, 2, 3, 5, 7, 4, 14, 19, 11, 6, 41, 55, 32, 16, 8, 122, 163, 95, 46, 21, 9, 365, 487, 284, 136, 60, 25, 10, 1094, 1459, 851, 406, 177, 73, 29, 12, 3281, 4375, 2552, 1216, 528, 217, 86, 34, 13, 9842, 13123, 7655, 3646, 1581, 649, 257, 100, 38, 15

Offset: 1

Clark Kimberling, Dec 15 2010

Joint-rank arrays are defined in the first comment at A182801.  As for any joint-rank array, A182949 is a permutation of the positive integers, but, a fortiori, A182949 is an interspersion: after initial terms every row is interspersed with all other rows.  The numbers (3*i+1)*3^j as an array comprise A182828; and sorted, A026225.
(row 1)=A007051.
(row 2)=A052919.
(col 1)=A182829.

			Northwest corner:
1....2....5....14...
3....7...19....55...
4...11...32....95...
6...16...46...136...

Clark Kimberling, Interspersions and Dispersions.

Cf. A182801, A182828, A026225, A182950.

 M[i_,j_]:=j+Floor[Log[3*i+1]/Log[3]]; T[i_,j_]:=Sum[Floor[2/3+(3*i+1)*3^(j-k-1)],{k,0,M[i,j]}]; TableForm[Table[T[i,j],{i,0,9},{j,0,9}]]

A201916 Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+2737)^2 = y^2.

Original entry on oeis.org

0, 75, 203, 323, 552, 708, 1020, 1127, 1311, 1428, 1608, 1820, 1955, 2336, 2675, 3128, 3311, 3627, 3927, 4140, 4508, 4743, 5535, 6003, 6800, 7280, 7848, 8211, 8588, 9240, 9860, 11063, 11895, 13583, 14168, 15180, 15827, 16827, 18011, 18768, 20915, 22836

Offset: 1

T. D. Noe, Feb 09 2012

Note that 2737 = 7 * 17 * 23, the product of the first three distinct primes in A058529 (and A001132) and hence the smallest such number. This sequence satisfies a linear difference equation of order 55 whose 55 initial terms can be found by running the Mathematica program.
There are many sequences like this one. What determines the order of the linear difference equation? All primes p have order 7. For those p, it appears that p^2 has order 11, p^3 order 15, and p^i order 3+4*i. It appears that for semiprimes p*q (with p > q), the order is 19. What is the next term of the sequence beginning 3, 7, 19, 55, 163? This could be sequence A052919, which is 1 + 2*3^f, where f is the number of primes.
The crossref list is thought to be complete up to Feb 14 2012.

Colin Barker, Table of n, a(n) for n = 1..1000

Cf. A001652 (1), A076296 (7), A118120 (17), A118337 (23), A118674 (31).
Cf. A129288 (41), A118675 (47), A118554 (49), A118673 (71), A129289 (73).
Cf. A118676 (79), A129298 (89), A129836 (97), A157119 (103), A161478 (113).
Cf. A129837 (119), A129992 (127), A129544 (137), A161482 (151).
Cf. A206426 (161), A130608 (167), A161486 (191), A185394 (193).
Cf. A129993 (199), A198294 (217), A130609 (223), A129625 (233).
Cf. A204765 (239), A129991 (241), A207058 (263), A129626 (281).
Cf. A205644 (287), A207059 (289), A129640 (313), A205672 (329).
Cf. A129999 (337), A118611 (343), A130610 (359), A207060 (401).
Cf. A129641 (409), A207061 (433), A130645 (439), A130004 (449).
Cf. A129642 (457), A129725 (521), A101152 (569), A130005 (577).
Cf. A207075 (479), A207076 (487), A207077 (497), A207078 (511).
Cf. A111258 (601), A115135 (617), A130013 (647), A130646 (727).
Cf. A122694 (761), A123654 (809), A129010 (833), A130647 (839).
Cf. A129857 (857), A130014 (881), A129974 (937), A129975 (953).
Cf. A130017 (967), A118630 (2401), A118576 (16807).

d = 2737; terms = 100; t = Select[Range[0, 55000], IntegerQ[Sqrt[#^2 + (#+d)^2]] &]; Do[AppendTo[t, t[[-1]] + 6*t[[-27]] - 6*t[[-28]] - t[[-54]] + t[[-55]]], {terms-55}]; t

a(n) = a(n-1) + 6*a(n-27) - 6*a(n-28) - a(n-54) + a(n-55), where the 55 initial terms can be computed using the Mathematica program.

G.f.: x^2*(73*x^53 +116*x^52 +100*x^51 +171*x^50 +104*x^49 +184*x^48 +57*x^47 +92*x^46 +55*x^45 +80*x^44 +88*x^43 +53*x^42 +139*x^41 +113*x^40 +139*x^39 +53*x^38 +88*x^37 +80*x^36 +55*x^35 +92*x^34 +57*x^33 +184*x^32 +104*x^31 +171*x^30 +100*x^29 +116*x^28 +73*x^27 -363*x^26 -568*x^25 -480*x^24 -797*x^23 -468*x^22 -792*x^21 -235*x^20 -368*x^19 -213*x^18 -300*x^17 -316*x^16 -183*x^15 -453*x^14 -339*x^13 -381*x^12 -135*x^11 -212*x^10 -180*x^9 -117*x^8 -184*x^7 -107*x^6 -312*x^5 -156*x^4 -229*x^3 -120*x^2 -128*x -75) / ((x -1)*(x^54 -6*x^27 +1)). - Colin Barker, May 18 2015

cp's OEIS Frontend

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