A091282 Exponent of 2 in prime(n)^2 - 1.

0, 3, 3, 4, 3, 3, 5, 3, 4, 3, 6, 3, 4, 3, 5, 3, 3, 3, 3, 4, 4, 5, 3, 4, 6, 3, 4, 3, 3, 5, 8, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 3, 7, 7, 3, 4, 3, 6, 3, 3, 4, 5, 5, 3, 9, 4, 3, 5, 3, 4, 3, 3, 3, 4, 4, 3, 3, 5, 3, 3, 6, 4, 5, 3, 3, 8, 3, 3, 5, 4, 3, 3, 5, 5, 4, 3, 7, 4, 3, 5, 3, 6, 4, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3

Offset: 1

Author

Labos Elemer, Jan 20 2004

Keywords

• nonn

Comments

Also, exponent of 2 in -1+prime(n)^s if s is an exponent of the form 4k+2 (previous definition). - Michel Marcus, Dec 20 2013

Primes that give records for this sequence can be found in A233930. - Michel Marcus, Dec 20 2013

Examples

			a(1)=0 since -1+2^s is always odd...
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007814, A023506, A023512, A091283, A091284.

Programs

Mathematica

IntegerExponent[Prime[Range[100]]^2 - 1, 2] (* Amiram Eldar, Jun 06 2024 *)

PARI

a(n) = valuation(prime(n)^2-1, 2); \\ Michel Marcus, Dec 20 2013

Formula

a(n) = A023506(n) + A023512(n). - Amiram Eldar, Jun 06 2024

Extensions

Definition modified by Michel Marcus, Dec 20 2013