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Number of decimal digits in the integer part of e^n.
2

%I #46 May 25 2024 16:58:43

%S 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,

%T 14,14,14,15,15,16,16,17,17,17,18,18,19,19,20,20,20,21,21,22,22,23,23,

%U 24,24,24,25,25,26,26,27,27,27,28,28,29,29,30,30,30,31,31,32,32,33,33

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

%H Benedict W. J. Irwin, <a href="/A254528/b254528.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = A055642(A000149(n)). - _Amiram Eldar_, May 25 2024

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

%t f[n_] := 1 + Floor@ Log10@ Exp@ n; Array[f, 75, 0]

%t Table[Sum[DigitCount[Floor[Exp[1]^k]][[n]], {n, 1, 10}], {k, 0, 150}] (* _Benedict W. J. Irwin_, Apr 13 2016 *)

%t IntegerLength[Floor[E^Range[0,80]]] (* _Harvey P. Dale_, Aug 28 2017 *)

%o (PARI) a(n) = localprec(n+1); #Str(floor(exp(n))); \\ _Michel Marcus_, Dec 05 2020

%Y Cf. A000149, A055642.

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

%K base,nonn

%O 0,4

%A _Robert G. Wilson v_, Feb 01 2015