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

1,3

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A004678, A035100.

Sequence in context: A092139 A084558 A320065 * A156875 A066339 A345379

Adjacent sequences: A163288 A163289 A163290 * A163292 A163293 A163294

Keyword

nonn,base

Author

Juri-Stepan Gerasimov, Jul 24 2009

Status

approved