A057159 Numbers k that divide s(k-1), where s(1) = 1, s(k) = s(k-1) + (k+1)*3^k.

4, 13, 35, 52, 95, 119, 169, 676, 11596, 57577, 159484, 276773, 360139, 1345747, 56193997, 60640957, 604170268, 807129973, 14161491721, 44013617932, 66076109593, 78910928161, 982436183855, 1969254547468, 36245496838135, 67108611933707, 153467508728387, 154850333611595, 951439847741159

Offset

1,1

Comments

{s(n)} = {1, 28, 136, 541, 1999, 7102, 24598, ...}; 4*s(n) = 3^(n+1)*(2n+1) - 23, with g.f. x*(-1-21*x+45*x^2) / ( (x-1)*(-1+3*x)^2 ). - R. J. Mathar, May 05 2018

Equivalently, numbers k > 1 such that 3^k == -23 (mod k) and (k mod 8) in {1,3,4,5,7}. Also contains 22592809054764364496642273453. - Max Alekseyev, Nov 15 2025

Links

Table of n, a(n) for n=1..29.

Mathematica

seq = RecurrenceTable[{s[n] == s[n - 1] + (n + 1)*3^n, s[1] == 1}, s, {n, 1, 20000}]; Select[Range[1, Length[seq]], Divisible[seq[[# - 1]], #] &] (* Vaclav Kotesovec, May 05 2018 *)

Crossrefs

Cf. A000244, A015949, A067945, A015973, A276671, A015888, A277288, A276740, A277628, A277289, A277126, A277630, A277340, A277274, A128148.

Sequence in context: A127981 A296303 A089453 * A189588 A266357 A095941

Adjacent sequences: A057156 A057157 A057158 * A057160 A057161 A057162

Keyword

nonn

Author

Robert G. Wilson v, Sep 13 2000

Extensions

Minor edits by Altug Alkan, May 05 2018

a(10)-a(12) from Vaclav Kotesovec, May 05 2018

a(13)-a(14) from Chai Wah Wu, Aug 26 2021

a(15)-a(16) from Chai Wah Wu, Sep 02 2021

a(17)-a(18) from Sean A. Irvine, May 25 2022

a(19)-a(29) from Max Alekseyev, Nov 15 2025

Status

approved