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Search: id:A035112
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| A035112 |
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Smallest even index 2a such that n-th irregular prime p (A000928(n)) divides Bernoulli_{2a} with 0<=2a<=p-3. |
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4
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| 32, 44, 58, 68, 24, 22, 130, 62, 84, 164, 100, 84, 20, 156, 88, 292, 280, 186, 100, 200, 382, 126, 240, 366, 196, 130, 94, 292, 400, 86, 270, 222, 52, 90, 22, 592, 522, 20, 428, 80, 236, 48, 224, 408, 628, 32, 12, 378, 290, 514, 260, 732, 220, 330, 544, 744, 102
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The ordered pair (p(n),a(n)) where p(n) is the n-th irregular prime is called an irregular pair. Some irregular primes, such as 157, are in more than one pair. See A091887 for the number of pairs for each irregular prime. See A092681 and A092682 for higher-order irregular pairs. - T. D. Noe (noe(AT)sspectra.com), Mar 03 2004
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REFERENCES
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L. C. Washington, Introduction to Cyclotomic Fields, Springer, p. 350.
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LINKS
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Eric Weisstein's World of Mathematics, Irregular Pair
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EXAMPLE
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The first irregular prime (37) divides the numerator (-7709321041217) of the 32_nd Bernoulli number.
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MATHEMATICA
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Do[ p = Prime[ n ]; k = 1; While[ 2*k < p - 3 && Mod[ Numerator[ BernoulliB[ 2*k ] ], p ] != 0, k++ ]; If[ 2*k != p - 3, Print[ 2*k ] ], { n, 3, 200} ]
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CROSSREFS
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Cf. A000928.
Sequence in context: A114042 A104390 A167528 this_sequence A167527 A114406 A114416
Adjacent sequences: A035109 A035110 A035111 this_sequence A035113 A035114 A035115
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), May 12 2001
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