A189683 Irregular pairs (p,2k) ordered by increasing k.

691, 12, 3617, 16, 43867, 18, 283, 20, 617, 20, 131, 22, 593, 22, 103, 24, 2294797, 24, 657931, 26, 9349, 28, 362903, 28, 1721, 30, 1001259881, 30, 37, 32, 683, 32, 305065927, 32, 151628697551, 34, 26315271553053477373, 36, 154210205991661, 38, 137616929, 40

Offset

1,1

Comments

The subsequence of irregular primes p is A046753.

Links

T. D. Noe, Table of n, a(n) for n = 1..132

Bernd C. Kellner, On irregular prime power divisors of the Bernoulli numbers, Math. Comp. 76 (2007), 405-441; arXiv:0409223 [math.NT], 2004.

B. Mazur, How can we construct abelian Galois extensions of basic number fields?, Bull. Amer. Math. Soc., 48 (2011), 155-209. See footnote 64 on p. 205.

Wikipedia, Regular prime: Irregular pairs.

Example

The first few irregular pairs are (691,12), (3617,16), (43867,18), (283,20), (617,20), (131,22), (593,22), ...

Mathematica

Flatten[Table[p = Select[First /@ FactorInteger[Abs[Numerator[BernoulliB[n]]]], # >= n+3 &]; Transpose[{p, Table[n, {Length[p]}]}], {n, 2, 70, 2}]] (* T. D. Noe, Apr 25 2011 *)

Crossrefs

Cf. A000367, A000928, A035112, A046753, A189684, A189685.

Sequence in context: A276594 A283301 A046988 * A029825 A180320 A159283

Adjacent sequences: A189680 A189681 A189682 * A189684 A189685 A189686

Keyword

nonn

Author

Jonathan Sondow, Apr 25 2011

Status

approved