cp's OEIS Frontend

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

%I A163291 #20 Dec 18 2016 01:46:40
%S A163291 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,
%T A163291 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,
%U A163291 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
%N A163291 Number of digits of n-th prime written in base 4.
%H A163291 G. C. Greubel, <a href="/A163291/b163291.txt">Table of n, a(n) for n = 1..1000</a>
%F A163291 a(n) = log_4 n + log_4 log n + O(1). - _Charles R Greathouse IV_, Mar 25 2010
%e A163291 6th prime = 13 = 31_4, so a(6) = 2;
%e A163291 7th prime = 17 = 101_4, so a(7) = 3;
%e A163291 54th prime = 251 = 3323_4, so a(54) = 4;
%e A163291 55th prime = 257 = 10001_4, so a(55) = 5.
%t A163291 IntegerLength[#, 4] & /@ Prime[Range[100]] (* _G. C. Greubel_, Dec 17 2016 *)
%o A163291 (PARI) a(n) = #digits(prime(n), 4); \\ _Michel Marcus_, Dec 18 2016
%Y A163291 Cf. A004678, A035100.
%K A163291 nonn,base
%O A163291 1,3
%A A163291 _Juri-Stepan Gerasimov_, Jul 24 2009