%I A119523
%S A119523 8,2,9,3,6,5,0,1,9,7,0,2,2,2,3,3,2,0,4,9,6,2,1,9,2,4,4,3,0,8,6,1,5,4,1,
%T A119523 6,7,3,1,5,4,8,4,7,6,2,7,5,8,3,3,9,5,5,7,3,6,4,9,0,8,2,8,9,7,7,2,8,1,9,
%U A119523 2,1,2,3,8,7,1,4,6,6,8,3,9,2,5,8,0,0,9,6,8,5,6,9,5,1,5,5,5,9
%N A119523 Decimal expansion of the van der Waerden-Ulam binary measure of the primes.
%C A119523 Decimal expansion of Sum_{ k >= 2} PrimePi[k]/2^k.
%C A119523 The primes have a larger measure than the composites as they dominate 
               the lower integers.
%C A119523 Binary JIS function (definition see e.g. A113829) for van der Waerden-Ulam 
               constant W (A119523)is given first differences of A000720 A000720(n+1)-A000720(n)=A010051(n+1)=JIS[W,
               2] where W=0.829365019702223320496219.. - Artur Jasinski (grafix(AT)csl.pl), 
               Jun 02 2008
%D A119523 S. M. Ulam, Problems in Modern Mathematics, John Wiley and Sons, New 
               York, 1960, page 54
%e A119523 .829365...
%t A119523 b = 0; Do[k = PrimePi[n + 1] - PrimePi[n]; b = b + k/2^n, {n, 1, 200}]; 
               First[RealDigits[N[b, 200]]] - Artur Jasinski (grafix(AT)csl.pl), 
               Jun 02 2008
%Y A119523 Cf. A000720, A119524 (measure of composites).
%Y A119523 Cf. A000720, A010051, A113829.
%Y A119523 Sequence in context: A085967 A143531 A019865 this_sequence A154212 A155035 
               A154189
%Y A119523 Adjacent sequences: A119520 A119521 A119522 this_sequence A119524 A119525 
               A119526
%K A119523 nonn,cons
%O A119523 0,1
%A A119523 Roger L. Bagula (rlbagultftn(AT)yahoo.com), May 27 2006
%E A119523 More terms from Peter Pein (petsie(AT)dordos.net), May 31 2006
%E A119523 Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 17 2006