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A069586
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Smallest prime power p^k (k>=2) such that there is a gap of exactly n between p^k and the next prime power q^l (l >= 2); or 0 if no such q^l exists.
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1
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8, 25, 125, 4, 4, 0, 9, 8, 16, 2187, 16, 4, 243, 0, 49, 9, 8, 9, 8, 0, 4, 27, 4, 8, 0, 0, 0, 4, 0, 6859, 0, 32, 16, 0, 0, 0, 27, 1331, 25, 9, 8, 0, 0, 81, 4, 243, 81, 16, 32, 0, 0, 0, 0, 27, 9, 8, 64, 0, 0, 4, 64, 0, 961, 64, 16, 0, 0, 0, 0, 0, 0, 9, 8, 169, 0, 49, 4, 0, 49, 0, 0, 0, 0, 0, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Any solution for the terms that are currently zero is > 10^14. Since there are so many 'missing' values, I would recommend leaving the more keyword. - Larry Reeves (larryr(AT)acm.org), Jul 02 2002
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EXAMPLE
| a(1) = 8 = 2^3 and 8+1 = 9=3^2; a(3) = 125 = 5^3 and 125 +3 =128 = 2^7.
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CROSSREFS
| First time a gap of n occurs in A025475 (with its initial 1 deleted).
Sequence in context: A135942 A181207 A068315 * A042189 A004246 A060718
Adjacent sequences: A069583 A069584 A069585 * A069587 A069588 A069589
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KEYWORD
| nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 24 2002
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EXTENSIONS
| More terms from Larry Reeves (larryr(AT)acm.org), Jul 02 2002
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