A035100 Number of bits in binary expansion of n-th prime.

2, 2, 3, 3, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Jamie Morken, Table of n, a(n) for n = 1..10000 (first 1000 terms from G. C. Greubel)

Crossrefs

Cf. A004676, A000523, A029837, A070939, A162145.

Programs

Maple

Digits := 40: [ seq(1+floor(evalf(log(ithprime(n))/log(2))), n=1..100) ];

Mathematica

f[n_]:=Length[IntegerDigits[Prime[n],2]]; Table[f[n],{n,5!}] (* Vladimir Joseph Stephan Orlovsky, Feb 07 2010 *)
IntegerLength[Prime[Range[100]],2] (* Harvey P. Dale, Nov 10 2022 *)

PARI

a(n)=#binary(prime(n)) \\ Charles R Greathouse IV, Sep 23 2012

Python

from sympy import prime
def A035100(n): return prime(n).bit_length() # Chai Wah Wu, Nov 19 2024