|
%I #3 Mar 31 2012 13:20:28
%S 1,1,5,19,305,1219,19505,78019,1248305,79891519,319566077,20452228927,
%T 327235662833,1308942651331,20943082421297,1340357274963007,
%U 85782865597632449,343131462390529795,21960413592993906881
%N Numerator of Sum[ (-1)^(k+1) * 1/2^Prime[k], {k,1,n} ].
%C Denominator of Sum[ (-1)^(k+1) * 1/2^Prime[k], {k,1,n} ] equals 2^Prime[n] = A034765[n]. a(n) is prime for n = {3,4,13,60,66,75,175,...} = A122151[n]. Prime a(n) are {5,19,327235662833,...} = A122152[n]. Parity Prime Constant C = Sum[ (-1)^(k+1) * 1/2^Prime[k], {k,1,Infinity} ]. C = limit[ a(n)/2^Prime[n], n->Infinity ] = 0.148809550788776224969568467866796531982224132808217067371770000563313912... Decimal expansion of Parity Prime Constant C is given in A122153[n]. Binary expansion of Primary Prime Constant C is given in A071986[n] = Mod[Pi[n], 2].
%F a(n) = Numerator[ Sum[ (-1)^(k+1) * 1/2^Prime[k], {k,1,n} ] ].
%t Table[Numerator[Sum[(-1)^(k+1)*1/2^Prime[k],{k,1,n}]],{n,1,30}]
%Y Cf. A034765, A122151, A122152, A122153, A071986, A000720.
%K frac,nonn
%O 1,3
%A _Alexander Adamchuk_, Aug 22 2006
|
