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A189683 Irregular pairs (p,2k) ordered by increasing k. 6
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 (list; graph; refs; listen; history; text; internal format)
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

B. C. Kellner, On irregular prime power divisors of the Bernoulli numbers, Math. Comp. 76 (2007), 405-441.

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, 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: A001067 A141590 A046988 * A029825 A180320 A159283

Adjacent sequences:  A189680 A189681 A189682 * A189684 A189685 A189686

KEYWORD

nonn

AUTHOR

Jonathan Sondow, Apr 25 2011

STATUS

approved

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Last modified October 25 23:29 EDT 2014. Contains 248566 sequences.