A319908 Lesser of twin primes pair p, such that the Mersenne numbers 2^p - 1 and 2^(p+2) - 1 have the same number of prime factors.

3, 5, 17, 71, 101, 137, 197, 269, 617, 857, 1019, 1049, 1061

Offset

1,1

Comments

The corresponding number of prime factors is 1, 1, 1, 3, 2, 2, 2, 2, 4, 4, 5, 4, 2, ...

Assuming that Mersenne numbers (2^p-1 with p prime) are always squarefree, the distinction between number of prime factors with multiplicity (A001222) and number of different prime factors (A001221) is inessential.

Links

Table of n, a(n) for n=1..13.

Example

3 is in the sequence since 3 and 5 are twin primes pair, and 2^3-1=7 and 2^5-1=31 are both primes, thus having the same number of prime factors.
71 is in the sequence since 71 and 73 are twin primes pair and 2^71-1 and 2^73-1 both have 3 prime factors.

Mathematica

Do[If[PrimeQ[n]&&PrimeQ[n+2]&&PrimeOmega[2^n-1]==PrimeOmega[2^(n+2)-1], Print[n]], {n, 1, 200}]

Prog

(PARI) isok(p) = isprime(p) && isprime(p+2) && (omega(2^p-1) == omega(2^(p+2)-1)); \\ Michel Marcus, Oct 02 2018

Crossrefs

Cf. A000225, A001359, A065341, A135975.

Sequence in context: A125957 A259908 A137460 * A356256 A232238 A102295

Adjacent sequences: A319905 A319906 A319907 * A319909 A319910 A319911

Keyword

nonn,more

Author

Amiram Eldar, Oct 01 2018

Status

approved