A262053 Euler pseudoprimes to base 6: composite integers such that abs(6^((n - 1)/2)) == 1 mod n.

185, 217, 301, 481, 1111, 1261, 1333, 1729, 2465, 2701, 3421, 3565, 3589, 3913, 5713, 6533, 8365, 10585, 11041, 11137, 12209, 14701, 15841, 17329, 18361, 20017, 21049, 22049, 29341, 31021, 31621, 34441, 36301, 38081, 39305, 39493, 41041, 43621, 44801, 46657

Offset: 1

Author

Daniel Lignon, Sep 09 2015

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..86 from Daniel Lignon)

Crossrefs

Cf. A006970 (base 2), A262051 (base 3), A262052 (base 5), this sequence (base 6), A262054 (base 7), A262055 (base 8).

Programs

Mathematica

eulerPseudoQ[n_?PrimeQ, b_] = False; eulerPseudoQ[n_, b_] := Block[{p = PowerMod[b, (n - 1)/2, n]}, p == Mod[1, n] || p == Mod[-1, n]]; Select[2 Range[25000] + 1, eulerPseudoQ[#, 6] &] (* Michael De Vlieger, Sep 09 2015, after Jean-François Alcover at A006970 *)

PARI

for(n=1, 1e5, if( Mod(6, (2*n+1))^n == 1 ||  Mod(6, (2*n+1))^n == 2*n && bigomega(2*n+1) != 1 , print1(2*n+1", "))); \\ Altug Alkan, Oct 11 2015