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

0,1

Links

Table of n, a(n) for n=0..59.

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

Example

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

Prog

(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")"))

Crossrefs

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

Sequence in context: A187949 A180161 A349243 * A103215 A037942 A008784

Adjacent sequences: A099258 A099259 A099260 * A099262 A099263 A099264

Keyword

nonn,base

Author

Rick L. Shepherd, Oct 11 2004

Extensions

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

Status

approved