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Search: id:A077761
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| A077761 |
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Decimal expansion of Mertens' constant, which is the limit of Sum{1/p(i), i=1..k } - log(log(p(k))) as k goes to infinity, where p(i) is the i-th prime number. |
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+0
3
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| 2, 6, 1, 4, 9, 7, 2, 1, 2, 8, 4, 7, 6, 4, 2, 7, 8, 3, 7, 5, 5, 4, 2, 6, 8, 3, 8, 6, 0, 8, 6, 9, 5, 8, 5, 9, 0, 5, 1, 5, 6, 6, 6, 4, 8, 2, 6, 1, 1, 9, 9, 2, 0, 6, 1, 9, 2, 0, 6, 4, 2, 1, 3, 9, 2, 4, 9, 2, 4, 5, 1, 0, 8, 9, 7, 3, 6, 8, 2, 0, 9, 7, 1, 4, 1, 4, 2, 6, 3, 1, 4, 3, 4, 2, 4, 6, 6, 5, 1, 0, 5, 1, 6, 1, 7
(list; cons; graph; listen)
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OFFSET
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0,1
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COMMENT
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Graham, Knuth & Patashnik incorrectly give this constant as 0.261972128. - Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 02 2005
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REFERENCES
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S. R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2004, pp. 94-98
R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, A Foundation For Computer Science, Addison-Wesley, Reading, MA, 1989, p. 23.
D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, 1996, Section VII.28, p. 257.
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LINKS
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Ph. Flajolet and I. Vardi, Zeta function expansions of some classical constants
Pieter Moree, Mathematical constants
P. Sebah and X. Gourdon, Constants from number theory
Torsten Sillke, The Harmonic Numbers and Series.
M. B. Villarino, Mertens' proof of Mertens' Theorem
Eric Weisstein's World of Mathematics, Mertens Constant
Eric Weisstein's World of Mathematics, Prime Zeta Function
Eric Weisstein's World of Mathematics, Harmonic Series of Primes
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FORMULA
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a(n)=A001620-sum(n=2,3,..infinity) zeta_prime(n)/n where the zeta prime sequence is A085548, A085541, A085964, A085965, A085966 etc. (Sebah and Gourdon) - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 29 2006
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EXAMPLE
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0.26149721284764278375542683860869585905156664826119920619206421392...
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CROSSREFS
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Sequence in context: A156146 A154584 A129677 this_sequence A076039 A019576 A141906
Adjacent sequences: A077758 A077759 A077760 this_sequence A077762 A077763 A077764
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KEYWORD
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cons,nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Nov 14 2002
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