This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A121240 #9 Feb 16 2025 08:33:02
%S A121240 1,3,13,53,849,3397,54353,217413,3478609,222630977,890523909,
%T A121240 56993530177,911896482833,3647585931333,58361374901329,
%U A121240 3735127993685057,239048191595843649,956192766383374597,61196337048535974209
%N A121240 Numerator of sum_{k=1..n} 1/2^prime(k).
%C A121240 a(n) is prime for n = {2, 3, 4, 10, 21, 321,..} where it takes the values {3, 13, 53, 222630977, ...}.
%C A121240 The prime constant A051006 = 0.414682509.. is limit(n->infinity) a(n)/2^prime(n) .
%H A121240 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeConstant.html">Prime Constant</a>.
%F A121240 a(n) = Numerator[ Sum[ 1/2^Prime[k], {k,1,n} ] ]. a(n) = A072762[ Prime[n] ].
%t A121240 Table[Numerator[Sum[1/2^Prime[k],{k,1,n}]],{n,1,30}]
%t A121240 Accumulate[1/2^Prime[Range[30]]]//Numerator (* _Harvey P. Dale_, Aug 11 2021 *)
%Y A121240 Cf. A034785 (denominators), A072762, A051006, A010051.
%K A121240 frac,nonn
%O A121240 1,2
%A A121240 _Alexander Adamchuk_, Aug 22 2006