A099261 Length in bits of (10^n)-th prime number.

2, 5, 10, 13, 17, 21, 24, 28, 31, 35, 38, 42, 45, 49, 52, 56, 59, 62, 66, 69, 73, 76, 79, 83, 86, 89, 93, 96, 100, 103, 106, 110, 113, 116, 120, 123, 127, 130, 133, 137, 140, 143, 147, 150, 153, 157, 160, 163, 167, 170, 173, 177, 180, 184, 187, 190, 194, 197, 200, 204

Offset: 0

Author

Rick L. Shepherd, Oct 11 2004

Keywords

• nonn
• base

Examples

			a(1) = 5 because A006988(1) = prime(10^1) = 29 = 11101 (base 2) has five bits.
		

Links

• Pierre Dusart, Estimates of Some Functions Over Primes Without R.H.

Crossrefs

Cf. A006988 ((10^n)-th prime), A006880 (pi(10^n)), A007053 (pi(2^n)), A099260 (decimal digit lengths).

Programs

PARI

a(n)=if(n<3,return([2,5,10][n+1]));my(l=n*log(10),ll=log(l),x=n*log(10)/log(2),lb=ceil(x+log(l+ll-1+(ll-2.2)/l)/log(2)),ub=ceil(x+log(l+ll-1+(ll-2)/l)/log(2)));if(lb==ub,lb,error("Cannot determine a("n")"))

Extensions

Extension, program, and reference from Charles R Greathouse IV, Aug 03 2010