A004002 Benford numbers: a(n) = e^e^...^e (n times) rounded to nearest integer.

1, 3, 15, 3814279

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

The next term, a(4) ~ 2.3315*10^1656520, has 1656521 decimal digits and is therefore too large to be included. [Rephrased by M. F. Hasler, May 01 2013]

Named by Turner (1991) after the American electrical engineer and physicist Frank Albert Benford, Jr. (1883-1948). - Amiram Eldar, Jun 26 2021

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• C. W. Clenshaw, F. W. J. Olver and P. R. Turner, Level-index arithmetic: An introductory survey in: P. R. Turner (ed.), Numerical Analysis and Parallel Processing, Lecture Notes in Mathematics, Vol. 1397, Springer, Berlin, Heidelberg, 1989, pp. 95-168.
• Peter R. Turner, Will the "real" real arithmetic please stand up?, Notices Amer. Math. Soc., Vol. 38 (1991), pp. 298-304; entire issue.
• Index entries for sequences related to Benford's law (The present sequence seems unrelated to Benford's law!)

Crossrefs

Cf. A056072, A225053.

Cf. A073236. - Melissa O'Neill, Jul 04 2015

Programs

Maple

p:= n-> `if`(n=0, 1, exp(1)^p(n-1)):
a:= n-> round(p(n)):
seq(a(n), n=0..3);  # Alois P. Heinz, Jul 20 2024

Mathematica

Round[NestList[Power[E, #] &, 1, 3]] (* Melissa O'Neill, Jul 04 2015 *)

Formula

a(n) = round(e^e^...^e), where e occurs n times, a(0) = 1 (= e^0). - Melissa O'Neill, Jul 04 2015