A023520 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,4

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

FORMULA

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

MAPLE

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

PROG

(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

CROSSREFS

Cf. A007814, A023515, A080378.

Sequence in context: A353364 A328390 A325599 * A103587 A306446 A100387

Adjacent sequences: A023517 A023518 A023519 * A023521 A023522 A023523

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

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

STATUS

approved