This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A189683 Irregular pairs (p,2k) ordered by increasing k. 7
 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: A276594 A283301 A046988 * A029825 A180320 A159283 Adjacent sequences:  A189680 A189681 A189682 * A189684 A189685 A189686 KEYWORD nonn AUTHOR Jonathan Sondow, Apr 25 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.