

A234535


Numbers n such that n1 is a divisor of 3^n + 5^n.


2



2, 3, 5, 9, 18, 39, 153, 222, 378, 630, 1685, 1749, 3003, 8178, 10422, 41310, 70338, 103833, 141669, 151590, 285390, 385578, 542793, 578589, 804870, 816750, 950418, 1105893, 1132830, 1583778, 1585710, 1972809, 2578719, 2642430, 3248583, 3628089, 5875230, 6116253, 6152495, 6469470, 8550738, 9231834
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OFFSET

1,1


COMMENTS

It is an open problem to find all numbers n such that (n+1)(n1) is a divisor of 3^n + 5^n.
Such n together with n^2 must belong to this sequence (an example is given by n=3). Furthermore, it is not known if the intersection of this sequence and A234536 equals {3}.  Max Alekseyev, May 19 2015


LINKS

Table of n, a(n) for n=1..42.
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[2, 10^6], Mod[PowerMod[3, #, #  1] + PowerMod[5, #, #  1], #  1] == 0 &]


CROSSREFS

Cf. A234536.
Sequence in context: A292541 A097332 A099236 * A320964 A130581 A051236
Adjacent sequences: A234532 A234533 A234534 * A234536 A234537 A234538


KEYWORD

nonn


AUTHOR

Siad Daboul, Dec 27 2013


STATUS

approved



