A023520 Exponent of 2 in prime factorization of prime(n)*prime(n-1) - 1.

0, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 3, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 3, 1, 1, 2, 1, 6, 2, 3

Offset: 2

Author

Clark Kimberling

Keywords

• nonn

Comments

a(n) = 1 if and only if A080378(n-1) = 2. - Robert Israel, Feb 07 2018

Links

• Robert Israel, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A007814, A023515, A080378.

Programs

Maple

seq(padic:-ordp(ithprime(n)*ithprime(n-1)-1,2),n=2..200); # Robert Israel, Feb 07 2018

PARI

a(n) = valuation(prime(n)*prime(n-1) - 1, 2); \\ Michel Marcus, Sep 30 2013

Python

from sympy import prime
def A023520(n): return (~(m:=prime(n)*prime(n-1)-1)& m-1).bit_length()    # Chai Wah Wu, Jul 07 2022

Formula

a(n) = A007814(A023515(n)). - Michel Marcus, Sep 30 2013

Extensions

Offset set to 2 and a(2) corrected by Michel Marcus, Sep 30 2013