A259368 - OEIS

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

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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 *)