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A164571
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Numbers n such that n and n+3 are prime powers.
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6
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1, 2, 4, 5, 8, 13, 16, 29, 61, 64, 125, 128, 509, 1021, 4093, 4096, 16381, 32768, 65536, 262144, 1048573, 4194301, 16777213, 268435456, 536870909, 1073741824, 36028797018963968
(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, 3) is a prime power pair.
n + (0, 2m), m >= 1, being an admissible pattern for prime pairs, since (0, 2m) = (0, 0) (mod 2), has high density.
n + (0, 2m-1), m >= 1, being a non-admissible pattern for prime pairs, since (0, 2m-1) = (0, 1) (mod 2), has low density [the only possible pairs are (2^a - 2m-1, 2^a) or (2^a, 2^a + 2m-1), a >= 0.]
n + (0, 3) being a non-admissible pattern for prime pairs, has only prime power pairs (2^a - 3, 2^a) or (2^a, 2^a + 3), a >= 0.
Numbers n such that n and n+3 are primes would give only 2, for the prime pair (2, 5).
10^18 < a(28) <= 19807040628566084398385987581. [From Donovan Johnson (donovan.johnson(AT)yahoo.com), Aug 17 2009]
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CROSSREFS
| Cf. 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: A023745 A178656 A085443 * A105134 A184775 A194415
Adjacent sequences: A164568 A164569 A164570 * A164572 A164573 A164574
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KEYWORD
| nonn
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AUTHOR
| Daniel Forgues (squid(AT)zensearch.com), Aug 16 2009
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EXTENSIONS
| Edited by Daniel Forgues (squid(AT)zensearch.com), Aug 17 2009
a(20)-a(27) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Aug 17 2009
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