A210435 Number of digits in 5^n.

1, 1, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 12, 13, 14, 14, 15, 16, 17, 17, 18, 19, 19, 20, 21, 21, 22, 23, 24, 24, 25, 26, 26, 27, 28, 28, 29, 30, 31, 31, 32, 33, 33, 34, 35, 35, 36, 37, 38, 38, 39, 40, 40, 41, 42, 42, 43, 44, 45, 45, 46, 47, 47

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Ana Rechtman, Octobre 2015, 3e Défi, Images des Mathématiques, CNRS, 2015 (in French).

Formula

a(n) = A055642(A000351(n)) = A055642(5^n) = floor(log_10(10*(5^n))). [Jonathan Vos Post, Mar 22 2012]

a(n) + A034887(n) = n+1. - Michel Marcus, Oct 27 2015

Example

a(4) = 3 because 5^4 = 625, which has 3 digits.
a(5) = 4 because 5^5 = 3125, which has 4 digits.

Maple

a:= n-> length(5^n): seq(a(n), n=0..100); # Alois P. Heinz, Mar 22 2012

Mathematica

Table[Length[IntegerDigits[5^n]], {n, 0, 67}] (* Bruno Berselli, Mar 22 2012 *)
IntegerLength[5^Range[0, 70]] (* Harvey P. Dale, Mar 26 2013 *)

Prog

(Magma) [#Intseq(5^n): n in [0..67]]; // Bruno Berselli, Mar 22 2012
(PARI) a(n) = #Str(5^n); \\ Michel Marcus, Oct 27 2015

Crossrefs

Cf. A000351, A055642.

Number of digits in b^n: A034887 (b=2), A034888 (b=3), A210434 (b=4), A210435 (b=5), A210436 (b=6), A210062 (b=7).

Sequence in context: A248103 A121928 A175406 * A181534 A258703 A067022

Adjacent sequences: A210432 A210433 A210434 * A210436 A210437 A210438

Keyword

nonn,base,easy

Author

Luc Comeau-Montasse, Mar 21 2012

Status

approved