A138761 a(n) is the smallest member of A000522 divisible by 2^n, where A000522(m) = total number of arrangements of a set with m elements.

1, 2, 16, 16, 16, 330665665962404000, 4216377920843140187197325631474390438452208808916276571342090223552

Offset

0,2

Comments

a(n) < A000522(2^n) for n > 0; see Sondow and Schalm, Proposition A.13 part (ii).

References

J. Sondow and K. Schalm, Which partial sums of the Taylor series for e are convergents to e? (and a link to the primes 2, 5, 13, 37, 463), Gems in Experimental Mathematics (T. Amdeberhan, L. A. Medina, and V. H. Moll, eds.), Contemporary Mathematics, vol. 517, Amer. Math. Soc., Providence, RI, 2010.

Links

Jean-François Alcover, Table of n, a(n) for n = 0..9

J. Sondow and K. Schalm, Which partial sums of the Taylor series for e are convergents to e? (and a link to the primes 2, 5, 13, 37, 463), II, arXiv:0709.0671 [math.NT], 2007-2009.

Index entries for sequences related to factorial numbers

Formula

a(n) = A000522(A127014(n)) = Sum_{k=0..A127014(n)} A127014(n)!/k! for n > 0.

Example

a(5) = A000522(19) = 330665665962404000 because that is the smallest member of A000522 divisible by 2^5.

Mathematica

a522[n_] := E Gamma[n + 1, 1];
(* b = A127014 *)
b[1] = 1; b[n_] := b[n] = For[k = b[n - 1], True, k++, If[Mod[a522[k], 2^n] == 0, Return[k]]];
a[0] = 1; a[n_] := a522[b[n]];
Table[a[n], {n, 0, 6}] (* Jean-François Alcover, Feb 20 2019 *)

Crossrefs

Cf. A000522, A127014, A127015.

Sequence in context: A110875 A263355 A066773 * A087970 A247634 A261617

Adjacent sequences: A138758 A138759 A138760 * A138762 A138763 A138764

Keyword

nonn

Author

Jonathan Sondow, Apr 01 2008

Status

approved