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

%I A085291 #45 Apr 01 2025 23:27:22
%S A085291 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,
%T A085291 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,
%U A085291 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
%N A085291 Decimal expansion of Alladi-Grinstead constant exp(c-1), where c is given in A085361.
%C A085291 Named after the Indian-American mathematician Krishnaswami Alladi (b. 1955) and the American mathematician Charles Miller Grinstead (b. 1952). - _Amiram Eldar_, Jun 15 2021
%D A085291 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, pp. 120-122.
%D A085291 R. K. Guy, Unsolved Problems in Number Theory, Springer, 1st edition, 1981. See section B22.
%H A085291 K. Alladi and C. Grinstead, <a href="http://dx.doi.org/10.1016/0022-314X(77)90006-3">On the decomposition of n! into prime powers</a>, J. Number Theory, Vol. 9, No. 4 (1977), pp. 452-458.
%H A085291 Simon Plouffe, <a href="http://www.plouffe.fr/simon/constants/alladig.txt">Alladi-Grinstead Constant</a>.
%H A085291 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Alladi-GrinsteadConstant.html">Alladi-Grinstead Constant</a>.
%H A085291 Wikipedia, <a href="https://en.wikipedia.org/wiki/Multiplicative_partitions_of_factorials">Multiplicative partitions of factorials</a>.
%F A085291 Equals exp(c-1), where c is Sum_{n>=1} (zeta(n+1) - 1)/n (cf. A085361).
%F A085291 Equals lim_{n->oo} (Product_{k=1..n} (k/n)*floor(n/k))^(1/n). - _Benoit Cloitre_, Jul 15 2022
%e A085291 0.80939402054063913071793188059409131721595399242500030424202871504...
%p A085291 evalf(exp(sum((Zeta(n+1)-1)/n, n=1..infinity)-1), 120); # _Vaclav Kotesovec_, Dec 11 2015
%t A085291 $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 *)
%o A085291 (PARI) exp(suminf(n=1, (zeta(n+1)-1)/n) - 1) \\ _Michel Marcus_, May 19 2020
%Y A085291 Cf. A085288, A085289, A085290, A085361.
%K A085291 nonn,cons
%O A085291 0,1
%A A085291 _Eric W. Weisstein_, Jun 25 2003
%E A085291 Corrected and extended by Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Jun 24 2003