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A121240 Numerator of sum_{k=1..n} 1/2^prime(k). 0
1, 3, 13, 53, 849, 3397, 54353, 217413, 3478609, 222630977, 890523909, 56993530177, 911896482833, 3647585931333, 58361374901329, 3735127993685057, 239048191595843649, 956192766383374597, 61196337048535974209 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

Table of n, a(n) for n=1..19.

Eric Weisstein's World of Mathematics, Prime Constant.

FORMULA

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

MATHEMATICA

Table[Numerator[Sum[1/2^Prime[k], {k, 1, n}]], {n, 1, 30}]

CROSSREFS

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

Sequence in context: A151209 A151210 A151211 * A065839 A066611 A180933

Adjacent sequences:  A121237 A121238 A121239 * A121241 A121242 A121243

KEYWORD

frac,nonn

AUTHOR

Alexander Adamchuk, Aug 22 2006

STATUS

approved

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Last modified November 21 05:01 EST 2017. Contains 294988 sequences.