A254528 Number of decimal digits in the integer part of e^n.

1, 1, 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 9, 10, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 14, 15, 15, 16, 16, 17, 17, 17, 18, 18, 19, 19, 20, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 24, 25, 25, 26, 26, 27, 27, 27, 28, 28, 29, 29, 30, 30, 30, 31, 31, 32, 32, 33, 33

Offset: 0

Author

Robert G. Wilson v, Feb 01 2015

Keywords

• base
• nonn

Examples

			e^10 = 22026.46579480671..., so a(10) = 5.
		

Links

• Benedict W. J. Irwin, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000149, A055642.

Cf. A001113, A072334, A091933, A092426, A092511, A092512, A092513 (see their offsets).

Programs

Mathematica

f[n_] := 1 + Floor@ Log10@ Exp@ n; Array[f, 75, 0]
Table[Sum[DigitCount[Floor[Exp[1]^k]][[n]], {n, 1, 10}], {k, 0, 150}] (* Benedict W. J. Irwin, Apr 13 2016 *)
IntegerLength[Floor[E^Range[0,80]]] (* Harvey P. Dale, Aug 28 2017 *)

PARI

a(n) = localprec(n+1); #Str(floor(exp(n))); \\ Michel Marcus, Dec 05 2020

Formula

a(n) = A055642(A000149(n)). - Amiram Eldar, May 25 2024