A098388 a(n) = floor(log_2(prime(n))).

1, 1, 2, 2, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 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, 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

Offset: 1

Author

Reinhard Zumkeller, Sep 06 2004

Keywords

• nonn
• easy

Comments

a(n) is the greatest k such that 2^k does not exceed prime(n). - David James Sycamore, Sep 14 2021

a(n) is the number of representations of prime(n) as a sum 2^m+r, where 1 <= r < prime(n): a(5) = 3 because prime(5) = 11 = 2^3 + 3 = 2^2 + 7 = 2^1 + 9. - Clark Kimberling, Feb 06 2025

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A000523, A023196, A035100, A098391.

Programs

Maple

map(ilog2, select(isprime,[2,seq(2*i+1,i=1..1000)])); # Robert Israel, Jun 08 2015

Mathematica

Floor[Log[2, Prime[Range[105]]]] (* data *) (* parameter changed by Hartmut F. W. Hoft, Jun 02 2015 *)

PARI

a(n) = logint(prime(n), 2); \\ Michel Marcus, Sep 17 2017

Python

from sympy import prime
def A098388(n): return prime(n).bit_length()-1 # Chai Wah Wu, Nov 19 2024

Formula

a(n) = A000523(A000040(n)); A098391(n) = A000523(a(n)).

a(n) = A035100(n) - 1. - Michel Marcus, Sep 17 2017