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A120431
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Numbers n such that n and n+2 are prime powers.
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6
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1, 2, 3, 5, 7, 9, 11, 17, 23, 25, 27, 29, 41, 47, 59, 71, 79, 81, 101, 107, 125, 137, 149, 167, 179, 191, 197, 227, 239, 241, 269, 281, 311, 347, 359, 419, 431, 461, 521, 569, 599, 617, 641, 659, 727, 809, 821, 827, 839, 857, 881, 1019, 1031, 1049, 1061, 1091
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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.]
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LINKS
| Daniel Forgues, Table of n, a(n) for n=1..1270
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EXAMPLE
| 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).
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MAPLE
| 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
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CROSSREFS
| 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 * A200049 A184017 A024195
Adjacent sequences: A120428 A120429 A120430 * A120432 A120433 A120434
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KEYWORD
| nonn
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AUTHOR
| Greg Huber (huber(AT)alum.mit.edu), Jul 13 2006
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EXTENSIONS
| 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
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