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Search: id:A119766
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| A119766 |
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Numbers n such that numerator of Bernoulli(n)/n is (apart from sign) 1 or a prime. |
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+0
3
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| 1, 2, 4, 6, 8, 10, 12, 14, 16, 18, 26, 34, 36, 38, 42, 74, 114, 118, 396, 674, 1870, 4306, 22808
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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In 1911 Ramanujan believed that the numerator of Bernoulli(n)/n for n even was (apart from sign) always either 1 or a prime. This is false.
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REFERENCES
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K. Ono, Honoring a gift from Kumbakonam, Notices Amer. Math. Soc., 53 (2006), 640-651.
S. Ramanujan, Some properties of Bernoulli's numbers, J. Indian Math. Soc., 3 (1911), 219-234.
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EXAMPLE
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As an example Bernoulli(20)/20= -174611/6600, but 174611=283*617. - Robert G. Wilson v Jun 22 2006.
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MAPLE
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A119766 := proc(nmax) local numr; for n from 2 to nmax by 2 do numr := abs(numer(bernoulli(n)/n)) ; if numr = 1 or isprime(numr) then print(n) ; fi ; od ; end : A119766(2000) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 21 2006
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MATHEMATICA
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OldPrimeQ[n_] := Abs[n]==1 || PrimeQ[Abs[n]]; Select[Range[2000], OldPrimeQ[Numerator[BernoulliB[ # ]/# ]] &] - T. D. Noe (noe(AT)sspectra.com), Jun 20 2006
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CROSSREFS
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Cf. A112548, A001067.
Sequence in context: A118070 A152966 A066122 this_sequence A030143 A110725 A100800
Adjacent sequences: A119763 A119764 A119765 this_sequence A119767 A119768 A119769
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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), Jun 19 2006
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EXTENSIONS
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a(21) and a(22) from T. D. Noe (noe(AT)sspectra.com), Jun 20 2006
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