A070192 Numbers k such that k divides the numerator of B(2k) (the Bernoulli numbers), but gcd(3k, 8^k+1) > 3.

301, 737, 1505, 1655, 2107, 3197, 3311, 3913, 5117, 5159, 5219, 5719, 6275, 6923, 7385, 7513, 7525, 8107, 8275, 8729, 9331, 9581, 9835, 10535, 10849, 11137, 11585, 12341, 12529, 12943, 13301, 14003, 14147, 14749, 15953, 15985, 17759, 18361

Offset: 1

Author

Benoit Cloitre and Dean Hickerson, Apr 26 2002

Keywords

• nonn

Comments

Equivalently, numbers that are in A069040 but not in A070191.

Links

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

Crossrefs

Cf. A027641, A069040, A070191, A070193.

Programs

Mathematica

testb[n_] := Select[First/@FactorInteger[n], Mod[2n, #-1]==0&]=={}; test8[n_] := GCD[3n, PowerMod[8, n, 3n]+1]==3; Select[Range[19000], testb[ # ]&&!test8[ # ]&]

PARI

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