A070193 Numbers k such that gcd(3k,8^k+1) = 3 but k does not divide the numerator of B(2k) (the Bernoulli numbers).

253, 1081, 1771, 2485, 2783, 3289, 4301, 4807, 5405, 5819, 7337, 7567, 7843, 9361, 10373, 10879, 11891, 12397, 12425, 13409, 13861, 14053, 14927, 15433, 17395, 17963, 18145, 18377, 18469, 19481, 19987, 20539, 20999, 22517, 23023, 24541

Offset: 1

Author

Benoit Cloitre and Dean Hickerson, Apr 26 2002

Keywords

• nonn

Comments

Equivalently, numbers is in A070191 but not in A069040.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A027641, A069040, A070191, A070192.

Programs

Mathematica

testb[n_] := Select[First/@FactorInteger[n], Mod[2n, #-1]==0&]=={}; test8[n_] := GCD[3n, PowerMod[8, n, 3n]+1]==3; Select[Range[25000], test8[ # ]&&!testb[ # ]&]

PARI

isA070191(k) = gcd(3*k, Mod(8, 3*k)^k + 1) == 3;
isok(k) = if(!isA070191(k), 0, my(p = factor(k)[,1]); for(i = 1, #p, if(!((2*k) % (p[i]-1)), return(1))); 0); \\ Amiram Eldar, Apr 24 2025