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A234536 Numbers k such that k+1 is a divisor of 3^k + 5^k. 3
1, 3, 7, 75, 2355, 11475, 31995, 57075, 80311, 196185, 215325, 335115, 991875, 1009545, 1038375, 1169715, 1185675, 1193655, 3507751, 5503095, 8412525, 8618475, 8670915, 9513075, 11384343, 12689415, 13587735, 13708695, 14101815, 14841255, 16002525, 17409015, 21856635, 22195875, 22307805, 25948755 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

It is an open problem to find all numbers k such that (k+1)*(k-1) is a divisor of 3^k + 5^k.

In particular, it is not known if the intersection of this sequence and A234535 equals {3}. - Max Alekseyev, May 19 2015

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..600

Daniel Kohen et al., On Polynomials dividing Exponentials, MathOverflow.

Byron Schmuland et al., Find all positive integers n such that 3^n + 5^n is divisible by n^2 - 1, Math StackExchange.

MATHEMATICA

Select[Range[10^6], Mod[PowerMod[3, #, # + 1] + PowerMod[5, #, # + 1], # + 1] == 0 &]

PROG

(PARI) isok(k) = Mod(3, k+1)^k + Mod(5, k+1)^k == 0; \\ Michel Marcus, Aug 04 2021

CROSSREFS

Cf. A234535.

Sequence in context: A119572 A172995 A325476 * A103737 A108537 A219292

Adjacent sequences:  A234533 A234534 A234535 * A234537 A234538 A234539

KEYWORD

nonn

AUTHOR

Siad Daboul, Dec 27 2013

EXTENSIONS

a(1) inserted by Amiram Eldar, Jul 31 2021

STATUS

approved

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Last modified October 20 12:21 EDT 2021. Contains 348106 sequences. (Running on oeis4.)