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A164573
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Numbers n such that n and n+5 are prime powers.
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6
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2, 3, 4, 8, 11, 27, 32, 59, 251, 1019, 2048, 4091, 262139, 1048571, 67108859, 4294967291, 68719476731, 140737488355328, 9007199254740992, 72057594037927931, 73786976294838206459, 332306998946228968225951765070086139
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OFFSET
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1,1
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COMMENTS
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Numbers n such that n + (0, 5) 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.]
Numbers n such that n and n+5 are primes would give only 2, for the prime pair (2, 7).
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LINKS
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PROG
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(PARI) v=List(); for(n=0, 1e3, if(isprimepower(2^n-5), listput(v, 2^n-5)); if(isprimepower(2^n+5), listput(v, 2^n))); Set(v) \\ Charles R Greathouse IV, Apr 24 2015
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CROSSREFS
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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.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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