A163291 Number of digits of n-th prime written in base 4.

1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

Offset: 1

Author

Juri-Stepan Gerasimov, Jul 24 2009

Keywords

• nonn
• base

Examples

			6th prime = 13 = 31_4, so a(6) = 2;
7th prime = 17 = 101_4, so a(7) = 3;
54th prime = 251 = 3323_4, so a(54) = 4;
55th prime = 257 = 10001_4, so a(55) = 5.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A004678, A035100.

Programs

Mathematica

IntegerLength[#, 4] & /@ Prime[Range[100]] (* G. C. Greubel, Dec 17 2016 *)

PARI

a(n) = #digits(prime(n), 4); \\ Michel Marcus, Dec 18 2016

Formula

a(n) = log_4 n + log_4 log n + O(1). - Charles R Greathouse IV, Mar 25 2010