A234536 -id:A234536 - cp's OEIS frontend

A276671 Positive integers k such that 3^k == 2 (mod k).

1, 2929, 9742277641, 23341869101, 15092205901438895, 16311037042239935

Offset: 1

Max Alekseyev, Oct 05 2016

No other terms below 2*10^16. A larger term: 31744873758348589012852097851.

Cf. A015973, A067945, A015949, A055686, A242865, A234535, A234536, A050259.

Join[{1}, Select[Range[10000], PowerMod[3, #, #] == 2 &]] (* Alonso del Arte, Oct 11 2016 *)

isok(n) = Mod(3, n)^n == Mod(2, n); \\ Dmitry Ezhov, Sep 28 2016

Order of terms corrected by Felix Fröhlich, Oct 06 2016

a(5)-a(6) from Sergey Paramonov, Oct 03 2021

A234535 Numbers n such that n-1 is a divisor of 3^n + 5^n.

Original entry on oeis.org

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

Offset: 1

Siad Daboul, Dec 27 2013

nonn

It is an open problem to find all numbers n such that (n+1)(n-1) 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

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

Cf. A234536.

Select[Range[2, 10^6], Mod[PowerMod[3, #, # - 1] + PowerMod[5, #, # - 1], # - 1] == 0 &]

cp's OEIS Frontend

A276671 Positive integers k such that 3^k == 2 (mod k).

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