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

0,1

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

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, pp. 120-122.

Links

Table of n, a(n) for n=0..101.

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.

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

Example

0.80939402054063913071793188059409131721595399242500030424202871504...

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 *)

Prog

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

Crossrefs

Cf. A085288, A085289, A085290, A085361.

Sequence in context: A246772 A198820 A138285 * A109219 A199506 A254178

Adjacent sequences: A085288 A085289 A085290 * A085292 A085293 A085294

Keyword

nonn,cons

Author

Eric W. Weisstein, Jun 25 2003

Extensions

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

Status

approved