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%I #8 Aug 11 2021 17:15:10
%S 1,3,13,53,849,3397,54353,217413,3478609,222630977,890523909,
%T 56993530177,911896482833,3647585931333,58361374901329,
%U 3735127993685057,239048191595843649,956192766383374597,61196337048535974209
%N Numerator of sum_{k=1..n} 1/2^prime(k).
%C a(n) is prime for n = {2, 3, 4, 10, 21, 321,..} where it takes the values {3, 13, 53, 222630977, ...}.
%C The prime constant A051006 = 0.414682509.. is limit(n->infinity) a(n)/2^prime(n) .
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeConstant.html">Prime Constant</a>.
%F a(n) = Numerator[ Sum[ 1/2^Prime[k], {k,1,n} ] ]. a(n) = A072762[ Prime[n] ].
%t Table[Numerator[Sum[1/2^Prime[k],{k,1,n}]],{n,1,30}]
%t Accumulate[1/2^Prime[Range[30]]]//Numerator (* _Harvey P. Dale_, Aug 11 2021 *)
%Y Cf. A034785 (denominators), A072762, A051006, A010051.
%K frac,nonn
%O 1,2
%A _Alexander Adamchuk_, Aug 22 2006
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