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

Author

Stefano Spezia, Nov 28 2024

Keywords

• nonn
• cons

Examples

			0.27317072236263839747106601431655151479129736936570...
		

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

• 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.

Crossrefs

Cf. A002162, A005597, A069205.

Programs

PARI

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

Formula

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