%I A077761
%S A077761 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,
%T A077761 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,
%U A077761 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
%N A077761 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.
%C A077761 Graham, Knuth & Patashnik incorrectly give this constant as 0.261972128. 
               - Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 02 2005
%D A077761 S. R. Finch, Mathematical Constants, Encyclopedia of Mathematics and 
               its Applications, vol. 94, Cambridge University Press, 2004, pp. 
               94-98
%D A077761 R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, A Foundation 
               For Computer Science, Addison-Wesley, Reading, MA, 1989, p. 23.
%D A077761 D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, 1996, Section 
               VII.28, p. 257.
%H A077761 Ph. Flajolet and I. Vardi, <a href="http://algo.inria.fr/flajolet/Publications/
               publist.html">Zeta function expansions of some classical constants</
               a>
%H A077761 Pieter Moree, <a href="http://web.inter.nl.net/hcc/J.Moree/linnumb.htm">
               Mathematical constants</a>
%H A077761 P. Sebah and X. Gourdon, <a href="http://numbers.computation.free.fr/
               Constants/constants.html">Constants from number theory</a>
%H A077761 Torsten Sillke, <a href="http://www.mathematik.uni-bielefeld.de/~sillke/
               PUZZLES/harmonic-series">The Harmonic Numbers and Series</a>.
%H A077761 M. B. Villarino, <a href="http://arXiv.org/abs/math.HO/0504289">Mertens' 
               proof of Mertens' Theorem </a>
%H A077761 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               MertensConstant.html">Mertens Constant</a>
%H A077761 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PrimeZetaFunction.html">Prime Zeta Function</a>
%H A077761 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HarmonicSeriesofPrimes.html">Harmonic Series of Primes</a>
%F A077761 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
%e A077761 0.26149721284764278375542683860869585905156664826119920619206421392...
%Y A077761 Sequence in context: A156146 A154584 A129677 this_sequence A076039 A019576 
               A141906
%Y A077761 Adjacent sequences: A077758 A077759 A077760 this_sequence A077762 A077763 
               A077764
%K A077761 cons,nonn
%O A077761 0,1
%A A077761 T. D. Noe (noe(AT)sspectra.com), Nov 14 2002