A091283 -id:A091283 - cp's OEIS frontend

A091284 Exponent of 2 in -1+prime[n]^s, if s is an exponent of form 16k-8. Except a(1)=0, a(n)=1+A091283(n).

0, 5, 5, 6, 5, 5, 7, 5, 6, 5, 8, 5, 6, 5, 7, 5, 5, 5, 5, 6, 6, 7, 5, 6, 8, 5, 6, 5, 5, 7, 10, 5, 6, 5, 5, 6, 5, 5, 6, 5, 5, 5, 9, 9, 5, 6, 5, 8, 5, 5

Offset: 1

Labos Elemer, Jan 22 2004

nonn

Exponents of 2 in -1+p^s if the exponent s[u]=(2^u)k-(2^(u-1) comes from other sequence generated with s[u-1] exponent by adding 1 to terms of the "previous" sequence. E.g. s=256k-128 needed an addition of 6 to the terms of A091282.

Cf. A023506, A007814, A091282, A091283, A090739, A090740, A090129.

Table[{8*k-4, Table[Part[Flatten[FactorInteger [ -1+Prime[n]^(16*k-8)]], 2], {n, 2, 50}]}, {k, 1, 2}]

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

Original entry on oeis.org

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

Labos Elemer, Jan 20 2004

nonn

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

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

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

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

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

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

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

Definition modified by Michel Marcus, Dec 20 2013

cp's OEIS Frontend

A091284 Exponent of 2 in -1+prime[n]^s, if s is an exponent of form 16k-8. Except a(1)=0, a(n)=1+A091283(n).

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

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