A125773 Numbers k that are not powers of 2 such that 2^k mod k = 2^k mod k^2; or A068535 with powers of 2 excluded.

35, 297, 1093, 2186, 2590, 3279, 3511, 4372, 5465, 6558, 7022, 7651, 8744, 9837, 10533, 10930, 13116, 14044, 14209, 21066, 23175, 24012, 24577, 26592, 28088, 31599, 35110, 38621, 42132, 49154, 987704, 3020871, 3074592, 18368834, 22655923, 105713883, 111503202, 1084277175

Offset: 1

Author

Alexander Adamchuk, Dec 07 2006

Keywords

• nonn

Comments

A068535 includes all powers of 2. a(3) = 1093 and a(7) = 3511 are the only known primes in this sequence. They belong to A001220 = Wieferich primes p: p^2 divides 2^(p-1) - 1. Note that most listed terms of this sequence are the multiples of Wieferich primes 1093 and 3511. No more terms in this sequence up to 6*10^6.

Crossrefs

Cf. A068535 (Numbers k such that 2^k mod k = 2^k mod k^2).

Cf. A001220 (Wieferich primes p: p^2 divides 2^(p-1) - 1).

Cf. A125774 (Numbers k such that 3^k mod k = 3^k mod k^2).

Cf. A125775 (Numbers k such that 5^k mod k = 5^k mod k^2).

Programs

Mathematica

Do[f=PowerMod[2,n,n];g=PowerMod[2,n,n^2];If[f==g&&!IntegerQ[Log[2,n]],Print[n]],{n,1,6000000}]

Extensions

More terms from Amiram Eldar, Jun 19 2022