A331374 Decimal expansion of Sum_{p prime} 1/(2^(p^2) - 1).

6, 8, 6, 2, 3, 6, 4, 3, 6, 3, 1, 4, 1, 8, 3, 3, 3, 3, 7, 8, 6, 7, 3, 7, 3, 8, 7, 8, 2, 8, 5, 6, 8, 4, 7, 6, 2, 0, 6, 5, 3, 5, 9, 5, 7, 3, 5, 0, 4, 5, 7, 0, 4, 6, 8, 5, 9, 4, 4, 2, 9, 5, 0, 4, 8, 5, 0, 2, 0, 5, 7, 1, 0, 4, 7, 0, 2, 4, 8, 9, 9, 0, 5, 8, 4, 4, 9

Offset

-1,1

Comments

This constant is irrational. Its irrationality is a consequence of a more general theorem proved by Erdős (1969).

Links

Table of n, a(n) for n=-1..85.

Daniel Duverney and Yohei Tachiya, Refinement of the Chowla-Erdős method and linear independence of certain Lambert series, Forum Mathematicum, Vol. 31. No. 6 (2019), pp. 1557-1566, alternative link.

Paul Erdős, On the irrationality of certain series, Math. Student, Vol. 36 (1969), pp. 222-226.

Example

0.06862364363141833337867373878285684762065359573504...

Mathematica

RealDigits[Sum[1/(2^(Prime[k]^2) - 1), {k, 1, 100}], 10, 100][[1]]

Prog

(PARI) suminf(k=1, 1/(2^prime(k)^2-1)) \\ Michel Marcus, May 03 2020

Crossrefs

Cf. A065442, A099772.

Sequence in context: A105798 A205650 A153755 * A340725 A021597 A331941

Adjacent sequences: A331371 A331372 A331373 * A331375 A331376 A331377

Keyword

nonn,cons

Author

Amiram Eldar, May 03 2020

Status

approved