

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.


0



3, 5, 17, 71, 101, 137, 197, 269, 617, 857, 1019, 1049, 1061
(list;
graph;
refs;
listen;
history;
text;
internal format)



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^p1 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 2^31=7 and 2^51=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 2^711 and 2^731 both have 3 prime factors.


MATHEMATICA

Do[If[PrimeQ[n]&&PrimeQ[n+2]&&PrimeOmega[2^n1]==PrimeOmega[2^(n+2)1], Print[n]], {n, 1, 200}]


PROG

(PARI) isok(p) = isprime(p) && isprime(p+2) && (omega(2^p1) == omega(2^(p+2)1)); \\ Michel Marcus, Oct 02 2018


CROSSREFS

Cf. A000225, A001359, A065341, A135975.
Sequence in context: A125957 A259908 A137460 * A232238 A102295 A227335
Adjacent sequences: A319905 A319906 A319907 * A319909 A319910 A319911


KEYWORD

nonn,more


AUTHOR

Amiram Eldar, Oct 01 2018


STATUS

approved



