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 A077761 Decimal expansion of Mertens' constant, which is the limit of (Sum_{i=1..k} 1/prime(i)) - log(log(prime(k))) as k goes to infinity, where prime(i) is the i-th prime number. 9
 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; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Graham, Knuth & Patashnik incorrectly give this constant as 0.261972128. - Robert G. Wilson v, Dec 02 2005 [This was corrected in the second edition (1994). - T. D. Noe, Mar 11 2017] REFERENCES 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. LINKS Christian Axler, New estimates for some functions defined over primes, Integers (2018) 18, Article #A52. Chris Caldwell, The Prime Pages, There are infinitely many primes, but, how big of an infinity? H. Cohen, High precision computation of Hardy-Littlewood constants, preprint, 1998. - From N. J. A. Sloane, Jan 26 2013 Pierre Dusart, Explicit estimates of some functions over primes, The Ramanujan Journal, 2016. 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. J. Sondow and K. MacMillan, Primary pseudoperfect numbers, arithmetic progressions, and the Erdos-Moser equation, Amer. Math. Monthly, 124 (2017) 232-240; arXiv:math/1812.06566 [math.NT], 2018. 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 FORMULA Equals A001620 - Sum_{n>=2} zeta_prime(n)/n where the zeta prime sequence is A085548, A085541, A085964, A085965, A085966 etc. [Sebah and Gourdon] - R. J. Mathar, Apr 29 2006 EXAMPLE 0.26149721284764278375542683860869585905156664826119920619206421392... MATHEMATICA \$MaxExtraPrecision = 400; RealDigits[ N[EulerGamma + NSum[(MoebiusMu[m]/m)*Log[N[Zeta[m], 120]], {m, 2, 1000}, Method -> "EulerMaclaurin", AccuracyGoal -> 120, NSumTerms -> 1000, PrecisionGoal -> 120, WorkingPrecision -> 120] , 120]][[1, 1 ;; 105]] (* or, from version 7 up: *) digits = 105; M = EulerGamma - NSum[ PrimeZetaP[n] / n, {n, 2, Infinity}, WorkingPrecision -> digits+10, NSumTerms -> 3*digits]; RealDigits[M, 10, digits] // First (* Jean-François Alcover, Mar 16 2011, updated Sep 01 2015 *) CROSSREFS Sequence in context: A192043 A154584 A129677 * A220406 A220794 A220959 Adjacent sequences:  A077758 A077759 A077760 * A077762 A077763 A077764 KEYWORD cons,nonn,changed AUTHOR T. D. Noe, Nov 14 2002 STATUS approved

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Last modified December 19 08:25 EST 2018. Contains 318245 sequences. (Running on oeis4.)