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

1,1

Comments

Equivalently, numbers is in A070191 but not in A069040.

Links

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

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[ # ]&]

Prog

(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

Crossrefs

Cf. A027641, A069040, A070191, A070192.

Sequence in context: A157356 A203085 A245790 * A054737 A123013 A183449

Adjacent sequences: A070190 A070191 A070192 * A070194 A070195 A070196

Keyword

nonn

Author

Benoit Cloitre and Dean Hickerson, Apr 26 2002

Status

approved