A250216 Weak irregular primes. A prime is weak irregular iff it is a Bernoulli irregular prime or an Euler irregular prime.

19, 31, 37, 43, 47, 59, 61, 67, 71, 79, 101, 103, 131, 137, 139, 149, 157, 193, 223, 233, 241, 251, 257, 263, 271, 277, 283, 293, 307, 311, 347, 349, 353, 359, 373, 379, 389, 401, 409, 419, 421, 433, 461, 463, 467, 491, 509, 523, 541, 547, 557, 563, 571, 577, 587, 593

Offset: 1

Author

Eric Chen, Dec 24 2014

Keywords

• nonn

Comments

Primes p which divide A241601(k) for some k.

Links

• Peter Luschny, Irregular Bernoulli and Euler Primes.
• The Prime Pages, Irregular Primes
• The Prime Pages, Euler Irregular

Crossrefs

Cf. A000928, A120337, A128197.

Programs

Mathematica

pmax = 593; m0 = 200; dm = 100;
b[n_] := Numerator[BernoulliB[2 n]/(2 n)];
c[n_] := Numerator[SeriesCoefficient[Log[Tan[x]+1/Cos[x]], {x, 0, 2n+1}]];
(* a1 = A241601 *) a1[0] = 1; a1[n_] := a1[n] = If[EvenQ[n], b[n/2] // Abs, c[(n - 1)/2]];
f[m_] := f[m] = Module[{}, aa = Table[a1[n], {n, 0, m}]; okQ[p_] := AnyTrue[aa, Divisible[#, p] &]; Reap[For[p = 2, p <= pmax, p = NextPrime[p], If[okQ[p], Sow[p]]]][[2, 1]]];
f[m = m0]; f[m = m + dm];
While[Print["m = ", m]; f[m] != f[m - dm], m = m + dm];
A250216 = f[m] (* Jean-François Alcover, Jul 23 2019 *)