1,2

Numbers n such that n + (0, 2) is a prime power pair.

Twin prime powers, a generalization of the twin primes. The twin primes are a subsequence.

n + (0, 2m), m >= 1, being an admissible pattern for prime pairs has high density.

n + (0, 2m-1), m >= 1, being a non-admissible pattern for prime pairs, has low density [the only possible pairs are (2^a - 2m-1, 2^a) or (2^a, 2^a + 2m-1), a >= 0.]

Daniel Forgues, Table of n, a(n) for n=1..1270

a(5)=7 since the 5th pair of twin prime powers is (7,9), while the first four pairs are (1,3), (2,4), (3,5) and (5,7).

isppow := proc(n) local pf; pf := ifactors(n)[2]; if nops(pf) = 1 or n =1 then true; else false; fi; end; isA120431 := proc(n) RETURN (isppow(n) and isppow(n+2)); end; for n from 1 to 1500 do if isA120431(n) then printf("%d, ", n); fi; od; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 16 2006

Cf. A001359, A000961.

Cf. A006549 Numbers n such that n and n+1 are prime powers.

Cf. A120431 Numbers n such that n and n+2 are prime powers.

Cf. A164571 Numbers n such that n and n+3 are prime powers.

Cf. A164572 Numbers n such that n and n+4 are prime powers.

Cf. A164573 Numbers n such that n and n+5 are prime powers.

Cf. A164574 Numbers n such that n and n+6 are prime powers.

Sequence in context: A139282 A066824 A036963 this_sequence A024195 A071423 A062781

Adjacent sequences: A120428 A120429 A120430 this_sequence A120432 A120433 A120434

nonn

Greg Huber (huber(AT)alum.mit.edu), Jul 13 2006

More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 16 2006

Additional comments from Daniel Forgues (squid(AT)zensearch.com), Aug 17 2009