A300762 Numbers k > 1 such that 2^k == 2 (mod k) and gcd(k, 3^k - 3) = 1.

35333, 42799, 49981, 60787, 150851, 162193, 164737, 241001, 253241, 256999, 280601, 452051, 481573, 556169, 617093, 665333, 722201, 838861, 1016801, 1252697, 1507963, 1534541, 1678541, 1826203, 2134277, 2269093, 2304167, 2313697, 2537641, 2617451, 2811271

Offset: 1

Author

Thomas Ordowski, Aug 15 2018

Keywords

• nonn

Comments

Numbers k > 1 such that 2^(k-1) == 1 (mod k) and gcd(k, 3^(k-1)-1) = 1.

Are there infinitely many such "anti-Carmichael pseudoprimes (2,3)"?

Crossrefs

Subsequence of A001567 and of A316907 and probably of A121707.

Programs

Mathematica

Select[Range[2 10^6], PowerMod[2, #, #] == 2 && GCD[#, # + PowerMod[3, #, #] - 3] == 1 &] (* Giovanni Resta, Aug 18 2018 *)

PARI

isok(k) = (k != 1) && (Mod(2, k)^k == Mod(2, k)) && (gcd(k, 3^k - 3) == 1); \\ Michel Marcus, Aug 15 2018

Extensions

More terms from Michel Marcus, Aug 15 2018

More terms from Giovanni Resta, Aug 18 2018