

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
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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), 405441.
B. Mazur, How can we construct abelian Galois extensions of basic number fields?, Bull. Amer. Math. Soc., 48 (2011), 155209. 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



