A259368 Number of digits in n^n when written in binary.

1, 3, 5, 9, 12, 16, 20, 25, 29, 34, 39, 44, 49, 54, 59, 65, 70, 76, 81, 87, 93, 99, 105, 111, 117, 123, 129, 135, 141, 148, 154, 161, 167, 173, 180, 187, 193, 200, 207, 213, 220, 227, 234, 241, 248, 255, 262, 269, 276, 283, 290, 297, 304, 311, 318, 326, 333

Offset: 1

Author

Adam J.T. Partridge, Jun 25 2015

Keywords

• nonn
• easy
• base

Examples

			For n=3, 3^3=11011_2 so a(3)=5.
		

Crossrefs

Cf. A000312, A066022, A070939.

Programs

Magma

[Floor(n*Log(n)/Log(2)) + 1: n in [1..70]]; // Vincenzo Librandi, Jul 15 2015

Mathematica

Array[IntegerLength[#^#, 2] &, 60] (* or *)
Array[Floor[# Log[2, #]] + 1 &, 60] (* Michael De Vlieger, Jul 03 2015 *)

PARI

a(n) = #binary(n^n); \\ Michel Marcus, Jul 03 2015

Formula

a(n) = floor(n*log(n)/log(2)) + 1.

a(n) = A070939(A000312(n)). - Michel Marcus, Jul 03 2015