A387506 Decimal expansion of Sum_{p prime} 1/p - log(1 + 1/p).

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

Offset

0,2

Comments

Because Sum_{n>=1} 1/n - log(1 + 1/n) = 0.577215664901532860606512... (A001620) this constant can be considered as a prime equivalent of the Euler-Mascheroni constant.

Links

Table of n, a(n) for n=0..104.

Formula

Equals A335089 + A143524. - Amiram Eldar, Sep 30 2025

Example

0.181981850416855270623292092851708578581...

Prog

(PARI)
suminf(n=2, sumeulerrat((-1/x)^n/n)) \\ Jason Yuen, Oct 01 2025

Crossrefs

Cf. A001620, A143524, A335089.

Sequence in context: A332079 A196765 A182526 * A298519 A238271 A217430

Adjacent sequences: A387503 A387504 A387505 * A387507 A387508 A387509

Keyword

nonn,cons

Author

Artur Jasinski, Sep 30 2025

Status

approved