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

1,2

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

Links

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

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A080038 A121937 A003034 * A202708 A027684 A276864

Adjacent sequences: A091279 A091280 A091281 * A091283 A091284 A091285

Keyword

nonn

Author

Labos Elemer, Jan 20 2004

Extensions

Definition modified by Michel Marcus, Dec 20 2013

Status

approved