A210436 Number of digits in 6^n.

1, 1, 2, 3, 4, 4, 5, 6, 7, 8, 8, 9, 10, 11, 11, 12, 13, 14, 15, 15, 16, 17, 18, 18, 19, 20, 21, 22, 22, 23, 24, 25, 25, 26, 27, 28, 29, 29, 30, 31, 32, 32, 33, 34, 35, 36, 36, 37, 38, 39, 39, 40, 41, 42, 43, 43, 44, 45, 46, 46, 47, 48, 49, 50, 50, 51, 52, 53

Offset: 0

Author

Luc Comeau-Montasse, Mar 21 2012

Keywords

• nonn
• base
• easy

Examples

			a(4) = 4 because 6^4 = 1296, which has 4 digits.
a(5) = 4 because 6^5 = 7776, which has 4 digits.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000400, A034887, A034888, A210062, A210434, A210435.

Programs

Magma

[#Intseq(6^n): n in [0..67]]; // Bruno Berselli, Mar 22 2012

Maple

a:= n-> length(6^n): seq (a(n), n=0..100); # Alois P. Heinz, Mar 22 2012

Mathematica

Table[Length[IntegerDigits[6^n]], {n, 0, 99}] (* Alonso del Arte, Mar 22 2012 *)

Formula

a(n) = A055642(A000400(n)) = A055642(6^n) = floor(log_10(10*(6^n))). - Jonathan Vos Post, Mar 23 2012