A023579 Exponent of 2 in prime factorization of prime(n)+3.

0, 1, 3, 1, 1, 4, 2, 1, 1, 5, 1, 3, 2, 1, 1, 3, 1, 6, 1, 1, 2, 1, 1, 2, 2, 3, 1, 1, 4, 2, 1, 1, 2, 1, 3, 1, 5, 1, 1, 4, 1, 3, 1, 2, 3, 1, 1, 1, 1, 3, 2, 1, 2, 1, 2, 1, 4, 1, 3, 2, 1, 3, 1, 1, 2, 6, 1, 2, 1, 5, 2, 1, 1, 3, 1, 1, 3, 4, 2, 2, 1, 3, 1, 2, 1, 1, 2, 2, 4, 1, 1, 1, 1, 1, 1, 1, 9, 2, 1

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Examples

			For n=1, prime(1)+3=5, and 5 is odd, so a(1)=0.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Programs

Magma

[Valuation(3+NthPrime(n), 2): n in [1..100]]; // G. C. Greubel, May 21 2019

Mathematica

Table[IntegerExponent[3 + Prime[n], 2], {n, 100}] (* G. C. Greubel, May 21 2019 *)

PARI

a(n) = valuation(prime(n)+3, 2); \\ Michel Marcus, Sep 30 2013

Python

from sympy import prime
def A023579(n): return (~(m:=prime(n)+3)& m-1).bit_length() # Chai Wah Wu, Jul 07 2022

Sage

[(nth_prime(n)+3).valuation(2) for n in (1..100)] # G. C. Greubel, May 21 2019

Formula

a(n) = A007814(A113935(n)). - Michel Marcus, Sep 30 2013

Extensions

a(1) corrected by Michel Marcus, Sep 30 2013

Name corrected by Charles R Greathouse IV, Mar 31 2014