A122150 Numerator of Sum[ (-1)^(k+1) * 1/2^Prime[k], {k,1,n} ].

1, 1, 5, 19, 305, 1219, 19505, 78019, 1248305, 79891519, 319566077, 20452228927, 327235662833, 1308942651331, 20943082421297, 1340357274963007, 85782865597632449, 343131462390529795, 21960413592993906881

Offset

1,3

Comments

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].

Links

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

Formula

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

Mathematica

Table[Numerator[Sum[(-1)^(k+1)*1/2^Prime[k], {k, 1, n}]], {n, 1, 30}]

Crossrefs

Cf. A034765, A122151, A122152, A122153, A071986, A000720.

Sequence in context: A362281 A092751 A357363 * A368888 A092663 A072526

Adjacent sequences: A122147 A122148 A122149 * A122151 A122152 A122153

Keyword

frac,nonn

Author

Alexander Adamchuk, Aug 22 2006

Status

approved