A100085 Decimal expansion of Sum_{n>0} 1/(n!^n!).

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

Offset: 1

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 08 2004

Keywords

• cons
• nonn

Comments

This number was called the Pomerance Number, after Carl Pomerance, in the paper by Bailey and Crandall referenced here. The paper by Martin contains a suggestion in its the Acknowledgements section by Carl Pomerance that the number might be "absolutely abnormal".

Examples

			1.250021433470507544581618655692730516577534706218865768307...
		

References

• G. Harman, One hundred years of normal numbers, in M. A. Bennett et al., eds., Number Theory for the Millennium, II (Urbana, IL, 2000), 149-166, A K Peters, Natick, MA, 2002.

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..10000.
• D. H. Bailey and R. E. Crandall, On the random character of fundamental constant expansions
• G. Martin, Absolutely abnormal numbers arXiv:math/0006089 [math.NT], 2000; American Mathematical Monthly 108 (October):746-754.

Crossrefs

Cf. A073009, A099870, A099871, A099872, A099873, A100084.

Programs

Mathematica

RealDigits[ Sum[1/(n!)^(n!), {n, 4}], 10, 111][[1]] (* Robert G. Wilson v, Feb 26 2008 *)

PARI

suminf(n=1, 1/(n!^n!)) \\ Michel Marcus, Dec 22 2016

Extensions

Edited by N. J. A. Sloane, May 16 2008 at the suggestion of R. J. Mathar