A378482 Decimal expansion of 1/(8*log(2)*A005597), where A005597 is the twin prime constant C_2.

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

Offset

0,1

References

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 2.5.1, p. 111.

Gérald Tenenbaum, Introduction to analytic and probabilistic number theory, Cambridge University Press, 1995, p. 53, exercise 5 (in the third edition 2015, p. 59, exercise 57).

Links

Table of n, a(n) for n=0..99.

Paul T. Bateman, Proof of a conjecture of Grosswald, Duke Mathematical Journal, Vol. 25. No. 1 (1958), pp. 67-72.

Emil Grosswald, The average order of an arithmetic function, Duke Mathematical Journal, Vol. 23, No. 1 (1956), pp. 41-44.

Formula

Equals lim_{n->oo} (1/(n*log(n)^2)) * A069205(n). - Amiram Eldar, Feb 15 2025

Example

0.27317072236263839747106601431655151479129736936570...

Prog

(PARI) 1/(8*log(2)*prodeulerrat(1-1/(p-1)^2, 1, 3)) \\ Amiram Eldar, Nov 29 2024

Crossrefs

Cf. A002162, A005597, A069205.

Sequence in context: A229952 A200439 A356381 * A197281 A019703 A124910

Adjacent sequences: A378479 A378480 A378481 * A378483 A378484 A378485

Keyword

nonn,cons

Author

Stefano Spezia, Nov 28 2024

Status

approved