cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A234536 Numbers k such that k+1 is a divisor of 3^k + 5^k.

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%I A234536 #25 Aug 04 2021 05:02:39
%S A234536 1,3,7,75,2355,11475,31995,57075,80311,196185,215325,335115,991875,
%T A234536 1009545,1038375,1169715,1185675,1193655,3507751,5503095,8412525,
%U A234536 8618475,8670915,9513075,11384343,12689415,13587735,13708695,14101815,14841255,16002525,17409015,21856635,22195875,22307805,25948755
%N A234536 Numbers k such that k+1 is a divisor of 3^k + 5^k.
%C A234536 It is an open problem to find all numbers k such that (k+1)*(k-1) is a divisor of 3^k + 5^k.
%C A234536 In particular, it is not known if the intersection of this sequence and A234535 equals {3}. - _Max Alekseyev_, May 19 2015
%H A234536 Amiram Eldar, <a href="/A234536/b234536.txt">Table of n, a(n) for n = 1..600</a>
%H A234536 Daniel Kohen et al., <a href="http://mathoverflow.net/questions/16341/on-polynomials-dividing-exponentials">On Polynomials dividing Exponentials</a>, MathOverflow.
%H A234536 Byron Schmuland et al., <a href="http://math.stackexchange.com/questions/612346">Find all positive integers n such that 3^n + 5^n is divisible by n^2 - 1</a>, Math StackExchange.
%t A234536 Select[Range[10^6], Mod[PowerMod[3, #, # + 1] + PowerMod[5, #, # + 1], # + 1] == 0 &]
%o A234536 (PARI) isok(k) = Mod(3, k+1)^k + Mod(5, k+1)^k == 0; \\ _Michel Marcus_, Aug 04 2021
%Y A234536 Cf. A234535.
%K A234536 nonn
%O A234536 1,2
%A A234536 _Siad Daboul_, Dec 27 2013
%E A234536 a(1) inserted by _Amiram Eldar_, Jul 31 2021