A004086 -id:A004086 - cp's OEIS frontend

A074864 a(n) = a(n-1) + a(n-2) + R(a(n-3)) + R(a(n-4)) where a(1)=a(2)=a(3)=a(4)=1 and R(n) (A004086) is the reverse of n.

1, 1, 1, 1, 4, 7, 13, 25, 49, 112, 244, 502, 1051, 2206, 3904, 7816, 19243, 37174, 66697, 144349, 292510, 563698, 1879315, 3401746, 6192718, 15630610, 33434152, 63708721, 106919440, 197375245, 342218854, 597294436, 1527006682, 3125687152

Offset: 1

Felice Russo, Sep 11 2002

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A000288, A074860, A074861, A074865.

RecurrenceTable[{a[1]==a[2]==a[3]==a[4]==1, a[n]==a[n-1]+a[n-2]+ IntegerReverse[ a[n-3]]+IntegerReverse[a[n-4]]},a,{n,40}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 10 2017 *)

More terms from Joshua Zucker, May 08 2006

Definition adapted to offset by Georg Fischer, Jun 18 2021

A074865 a(n) = a(n-1) + R(a(n-2)) + R(a(n-3)) + R(a(n-4)) where a(1) = a(2) = a(3) = a(4) = 1 and R(n) (A004086) is the reverse of n.

Original entry on oeis.org

1, 1, 1, 1, 4, 7, 13, 25, 67, 157, 316, 1195, 2635, 9910, 21796, 33268, 108541, 264685, 566431, 1384927, 2251855, 10267813, 23278831, 68031385, 119376340, 223452859, 339327088, 1399568407, 3282220573, 12169858759, 23849465446, 130434244321, 294426858097

Offset: 1

Felice Russo, Sep 11 2002

Cf. A000288, A004086.

a[1]=a[2]=a[3]=a[4]=1; R[n_]:=FromDigits[Reverse[IntegerDigits[n]]]; a[n_]:=a[n-1]+R[a[n-2]]+R[a[n-3]]+R[a[n-4]]; Array[a,32] (* Stefano Spezia, Jun 14 2023 *)

Corrected and extended by Michel ten Voorde Jun 13 2003
More terms from Joshua Zucker, May 08 2006
Definition adapted to offset by Georg Fischer, Jun 18 2021

A075605 Smallest k not a palindrome and not divisible by 10 such that k and R(k) (A004086) both are divisible by the n-th prime.

Original entry on oeis.org

24, 12, 5015, 168, 132, 1495, 1156, 2166, 3358, 2784, 1178, 1332, 1066, 13803, 1692, 2544, 13098, 27633, 6097, 67947, 10293, 103569, 13778, 19936, 22407, 1212, 21527, 20437, 10246, 22487, 141478, 1572, 100969, 15707, 15347, 72178, 39407, 336106

Offset: 1

Amarnath Murthy, Sep 28 2002

Cf. A004086, A075606.

More terms from David Wasserman, Jan 24 2005

A083447 a(n) = floor( n*R(n)/(n+R(n))), where R(n) is the digit reversal of n (A004086).

Original entry on oeis.org

1, 1, 2, 2, 3, 3, 4, 4, 0, 5, 7, 9, 10, 11, 12, 13, 14, 15, 1, 7, 11, 13, 15, 16, 18, 19, 20, 22, 2, 9, 13, 16, 18, 21, 22, 24, 26, 27, 3, 10, 15, 18, 22, 24, 26, 28, 30, 32, 4, 11, 16, 21, 24, 27, 30, 32, 34, 36, 5, 12, 18, 22, 26, 30, 33, 35, 37, 40, 6, 13, 19, 24, 28, 32, 35, 38, 41

Offset: 2

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 01 2003

			a(17) = floor(17*71/(17+71)) = floor(1207/88) = 13.

Vincenzo Librandi, Table of n, a(n) for n = 2..1000

Cf. A004086.

drev[n_]:=Module[{dr=FromDigits[Reverse[IntegerDigits[n]]]},Floor[ (dr*n)/ (dr+n)]]; Array[drev,80,2] (* Harvey P. Dale, Apr 26 2014 *)

More terms from Jason Earls, May 23 2004

A103161 GCD of reverse(2^n) and reverse(2^(n+1)), where reverse(k) = A004086(k), the decimal representation of k read backwards.

Original entry on oeis.org

2, 4, 1, 1, 23, 1, 1, 1, 1, 4201, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 7, 1, 1, 1, 1, 4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 19, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 34, 1, 1, 1, 7, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Labos Elemer, Jan 25 2005

			n=10: GCD of backward written powers of 2 is GCD(4201, 8402) = 4201 = a(10).

Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A000079, A004094.

rd[x_] :=FromDigits[Reverse[IntegerDigits[x]]] Table[GCD[rd[2^w], rd[2^(w+1)]], {w, 1, 100}]
GCD[IntegerReverse[#[[1]]],IntegerReverse[#[[2]]]]&/@ Partition[ 2^Range[110],2,1] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 24 2017 *)

rev(n) = subst(Polrev(digits(n)), 'x, 10); \\ These two functions from Charles R Greathouse IV, Oct 20 2014
A004094(n) = rev(2^n);
A103161(n) = gcd(A004094(n),A004094(1+n)); \\ Antti Karttunen, Dec 07 2017

a(n) = gcd(A004094(n), A004094(n+1)).

A191221 Numbers k such that k plus the sum of the digits of k is prime, and R(k) plus the sum of the digits of k is prime, where R(k) = A004086(k).

Original entry on oeis.org

1, 10, 11, 19, 35, 37, 53, 59, 73, 91, 95, 100, 101, 143, 181, 218, 232, 250, 272, 296, 298, 323, 341, 343, 365, 383, 385, 418, 436, 454, 490, 509, 527, 547, 563, 583, 610, 634, 650, 656, 670, 692, 725, 727, 745, 749, 767, 787, 812, 814, 838, 850, 892, 905, 947, 949, 1009

Offset: 1

Carmine Suriano, May 27 2011

Numbers ending with zero(s) when reversed have fewer digits.

			143 and 341 belong to the sequence since 143 + (1+4+3) = 151 is prime and 341 + (3+4+1) = 349 is also a prime.

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Cf. A004086, A007953.

read(transforms): isA191221 := proc(n) local r: r:=digrev(n): return (isprime(n+digsum(n)) and isprime(r+digsum(r))): end: A191221 := proc(n) option remember: local k: if(n=1)then return 1: fi: for k from procname(n-1)+1 do if(isA191221(k))then return k: fi: od: end: seq(A191221(n),n=1..57); # Nathaniel Johnston, May 27 2011

nrQ[n_]:=Module[{idn=IntegerDigits[n],t},t=Total[idn];And@@PrimeQ[{n+t, FromDigits[Reverse[idn]]+t}]]; Select[Range[1200],nrQ] (* Harvey P. Dale, Feb 24 2013 *)

A209915 Number of ways the n-th prime p(n) can be written as a multiple of its reversal A004086(p) +/- a prime q < p(n).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 0, 4, 0, 3, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 2, 4, 0, 0, 0, 0, 0, 2

Offset: 1

M. F. Hasler, Mar 15 2012

Sequence A209063 is a subsequence which contains all (but not only) nonzero terms.

Cf. A209063.

a(n)={my(r=A004086(n=prime(n))); sum(k=1, (2*n-1)\r, isprime(abs(n-k*r)))}

A209915 = A209914 o A000040.

A232183 Primes p such that p-R(p) is a square, where R = reversal of digits = A004086.

Original entry on oeis.org

2, 3, 5, 7, 11, 43, 73, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 2141, 2251, 4253, 4363, 4583, 6701, 7211, 7321, 7541, 8147, 8923, 9103, 9323, 9433, 10301, 10501, 10601, 11311, 11411, 12421, 12721, 12821, 13331, 13831, 13931, 14341, 14741

Offset: 1

M. F. Hasler, Nov 20 2013

This sequence includes the palindromic primes for which p-R(p)=0. See A080177 = (43,73,2141,2251,4253,4363,...) for the variant not including palindromes.

Archimedes' Lab, What is special about this number? - 43.

forprime(p=1,19999,issquare(p-A004086(p))&&print1(p","))

A257842 Semiprimes pq such that R(pq) = R(p)*R(q), where R = A004086 = reverse digits.

Original entry on oeis.org

4, 6, 9, 22, 26, 33, 39, 46, 55, 62, 69, 77, 82, 86, 93, 121, 143, 169, 187, 202, 206, 226, 253, 262, 299, 303, 309, 339, 341, 393, 422, 446, 451, 466, 473, 482, 505, 583, 622, 626, 633, 662, 669, 671, 699, 707, 781, 802, 842, 862, 866, 886, 933, 939, 961

Offset: 1

M. F. Hasler, May 11 2015

A subsequence of A161600. Almost all terms with less than 4 digits are either multiples of 2 or 3 or of 11.

Giovanni Resta, Table of n, a(n) for n = 1..10000

Cf. A161600, A071786, A004086.

N:= 1000: # to get all terms <= N
digrev:= proc(n) local L,i;
L:= convert(n,base,10);
add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
F:= proc(p,q) if digrev(p*q)=digrev(p)*digrev(q) then p*q else NULL fi end proc:
sort([seq(seq(F(Primes[i],q), q = select(`<=`,Primes[i..-1],N/Primes[i])), i=1..nops(Primes))]); # Robert Israel, May 14 2015

f[n_]:=FactorInteger[n][[1,1]];g[n_]:=FromDigits[Reverse[IntegerDigits[n]]];Select[Range@1000,PrimeOmega[#]==2&&g[f[#]*#/f[#]]==g[f[#]]*g[#/f[#]]&] (* Ivan N. Ianakiev, May 14 2015 *)

is(n)=bigomega(n)==2&&!eval(concat(Vecrev(Str(n"-"vecmin(n=factor(n)[,1])"*"vecmax(n)))))

A260874 Smallest prime of the form p//r//p//r//p//r// ...., where p = prime(n), r = A004086(p) and // denotes concatenation.

Original entry on oeis.org

1331133113, 17711771177117711771177117711771177117711771177117711771177117711771177117, 19911991199119, 23322332233223322332233223322332233223322332233223322332233223322332233223322332233223322332233223322332233223322332233223, 2992299229, 31133113311331

Offset: 6

Felix Fröhlich, Aug 02 2015

Felix Fröhlich, Table of n, a(n) for n = 6..100

Cf. A067087, A110408.

a(n) = p=prime(n); r=eval(concat(Vecrev(Str(p)))); s=eval(Str(p, r)); i=0; while(!ispseudoprime(s), if(i%2==0, s=eval(Str(s, p)); i++, s=eval(Str(s, r)); i++)); s

cp's OEIS Frontend

A074864 a(n) = a(n-1) + a(n-2) + R(a(n-3)) + R(a(n-4)) where a(1)=a(2)=a(3)=a(4)=1 and R(n) (A004086) is the reverse of n.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Extensions

A074865 a(n) = a(n-1) + R(a(n-2)) + R(a(n-3)) + R(a(n-4)) where a(1) = a(2) = a(3) = a(4) = 1 and R(n) (A004086) is the reverse of n.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Extensions

A075605 Smallest k not a palindrome and not divisible by 10 such that k and R(k) (A004086) both are divisible by the n-th prime.

Views

Author

Keywords

Crossrefs

Extensions

A083447 a(n) = floor( n*R(n)/(n+R(n))), where R(n) is the digit reversal of n (A004086).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

Extensions

A103161 GCD of reverse(2^n) and reverse(2^(n+1)), where reverse(k) = A004086(k), the decimal representation of k read backwards.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A191221 Numbers k such that k plus the sum of the digits of k is prime, and R(k) plus the sum of the digits of k is prime, where R(k) = A004086(k).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

A209915 Number of ways the n-th prime p(n) can be written as a multiple of its reversal A004086(p) +/- a prime q < p(n).

Views

Author

Keywords

Comments

Crossrefs

Programs

PARI

Formula

A232183 Primes p such that p-R(p) is a square, where R = reversal of digits = A004086.

Views

Author

Keywords

Comments

Links

Programs

PARI

A257842 Semiprimes p*q such that R(p*q) = R(p)*R(q), where R = A004086 = reverse digits.

Views

Author

Keywords

Comments

Links

Crossrefs

A257842 Semiprimes pq such that R(pq) = R(p)*R(q), where R = A004086 = reverse digits.