A085291 Decimal expansion of Alladi-Grinstead constant exp(c-1), where c is given in A085361.

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

Offset: 0

Author

Eric W. Weisstein, Jun 25 2003

Keywords

• nonn
• cons

Comments

Named after the Indian-American mathematician Krishnaswami Alladi (b. 1955) and the American mathematician Charles Miller Grinstead (b. 1952). - Amiram Eldar, Jun 15 2021

Examples

			0.80939402054063913071793188059409131721595399242500030424202871504...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, pp. 120-122.
• R. K. Guy, Unsolved Problems in Number Theory, Springer, 1st edition, 1981. See section B22.

Links

• K. Alladi and C. Grinstead, On the decomposition of n! into prime powers, J. Number Theory, Vol. 9, No. 4 (1977), pp. 452-458.
• Simon Plouffe, Alladi-Grinstead Constant.
• Eric Weisstein's World of Mathematics, Alladi-Grinstead Constant.
• Wikipedia, Multiplicative partitions of factorials.

Crossrefs

Cf. A085288, A085289, A085290, A085361.

Programs

Maple

evalf(exp(sum((Zeta(n+1)-1)/n, n=1..infinity)-1), 120); # Vaclav Kotesovec, Dec 11 2015

Mathematica

$MaxExtraPrecision = 256; RealDigits[ Exp[ Sum[ N[(-1 + Zeta[1 + n])/n, 256], {n, 350}] - 1], 10, 111][[1]] (* Robert G. Wilson v, Nov 23 2005 *)

PARI

exp(suminf(n=1, (zeta(n+1)-1)/n) - 1) \\ Michel Marcus, May 19 2020

Formula

Equals exp(c-1), where c is Sum_{n>=1} (zeta(n+1) - 1)/n (cf. A085361).

Equals lim_{n->oo} (Product_{k=1..n} (k/n)*floor(n/k))^(1/n). - Benoit Cloitre, Jul 15 2022

Extensions

Corrected and extended by Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Jun 24 2003