A068504 Highest power of 2 dividing prime(n)+1.

1, 4, 2, 8, 4, 2, 2, 4, 8, 2, 32, 2, 2, 4, 16, 2, 4, 2, 4, 8, 2, 16, 4, 2, 2, 2, 8, 4, 2, 2, 128, 4, 2, 4, 2, 8, 2, 4, 8, 2, 4, 2, 64, 2, 2, 8, 4, 32, 4, 2, 2, 16, 2, 4, 2, 8, 2, 16, 2, 2, 4, 2, 4, 8, 2, 2, 4, 2, 4, 2, 2, 8, 16, 2, 4, 128, 2, 2, 2, 2, 4, 2, 16, 2, 8, 4, 2, 2, 2, 16, 4, 32, 8, 4, 4, 8, 2

Offset: 1

Author

Benoit Cloitre, Mar 11 2002

Keywords

• easy
• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006519, A008864, A023512.

Programs

Maple

f:= n -> 2^padic:-ordp(ithprime(n)+1,2):
map(f, [$1..100]); # Robert Israel, Jan 13 2017

Mathematica

a[n_] := 2^IntegerExponent[Prime[n] + 1, 2]; Array[a, 100] (* Amiram Eldar, Jun 04 2022 *)

PARI

a(n) = 2^valuation(prime(n)+1, 2); \\ Michel Marcus, Nov 24 2013

Python

from sympy import prime
def A068504(n): return (m:=prime(n)+1)&-m # Chai Wah Wu, Jul 09 2022

Formula

a(n) = A006519(A008864(n)). - Michel Marcus, Nov 24 2013

a(n) = 2^A023512(n). - Michel Marcus, Nov 24 2013