A121240 Numerator of sum_{k=1..n} 1/2^prime(k).

1, 3, 13, 53, 849, 3397, 54353, 217413, 3478609, 222630977, 890523909, 56993530177, 911896482833, 3647585931333, 58361374901329, 3735127993685057, 239048191595843649, 956192766383374597, 61196337048535974209

Offset: 1

Author

Alexander Adamchuk, Aug 22 2006

Keywords

• frac
• nonn

Comments

a(n) is prime for n = {2, 3, 4, 10, 21, 321,..} where it takes the values {3, 13, 53, 222630977, ...}.

The prime constant A051006 = 0.414682509.. is limit(n->infinity) a(n)/2^prime(n) .

Links

• Eric Weisstein's World of Mathematics, Prime Constant.

Crossrefs

Cf. A034785 (denominators), A072762, A051006, A010051.

Programs

Mathematica

Table[Numerator[Sum[1/2^Prime[k],{k,1,n}]],{n,1,30}]
Accumulate[1/2^Prime[Range[30]]]//Numerator (* Harvey P. Dale, Aug 11 2021 *)

Formula

a(n) = Numerator[ Sum[ 1/2^Prime[k], {k,1,n} ] ]. a(n) = A072762[ Prime[n] ].