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

1,2

Links

Table of n, a(n) for n=1..57.

Formula

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

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

Example

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

Mathematica

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

Prog

(PARI) a(n) = #binary(n^n); \\ Michel Marcus, Jul 03 2015
(Magma) [Floor(n*Log(n)/Log(2)) + 1: n in [1..70]]; // Vincenzo Librandi, Jul 15 2015

Crossrefs

Cf. A000312, A066022, A070939.

Sequence in context: A006282 A086845 A243205 * A175098 A351389 A242067

Adjacent sequences: A259365 A259366 A259367 * A259369 A259370 A259371

Keyword

nonn,easy,base

Author

Adam J.T. Partridge, Jun 25 2015

Status

approved