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

1,1

Comments

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

Links

Table of n, a(n) for n=1..56.

Peter Luschny, Irregular Bernoulli and Euler Primes.

The Prime Pages, Irregular Primes

The Prime Pages, Euler Irregular

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 *)

Crossrefs

Cf. A000928, A120337, A128197.

Sequence in context: A316678 A330275 A038672 * A125148 A214798 A040066

Adjacent sequences: A250213 A250214 A250215 * A250217 A250218 A250219

Keyword

nonn

Author

Eric Chen, Dec 24 2014

Status

approved