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A023056
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a(n) is least k such that k and k+n are adjacent nontrivial powers of positive integers, or 0 if no such k apparently exists.
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5
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8, 25, 1, 4, 27, 0, 9, 97336, 16, 2187, 3125, 2197, 36, 0, 49, 128, 64, 225, 81, 196, 100, 0, 2025, 1000, 144, 42849, 169, 484, 0, 6859, 0, 7744, 256, 0, 289, 1728, 14348907, 1331, 361, 2704, 400, 0, 441, 0, 9216, 0, 529, 21904, 576, 0, 625, 0, 676, 0, 729, 5776, 784, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Searching up to 10^22, the largest term for n <= 1000 is a(618) = 421351^3 = 74805251419106551. - T. D. Noe, Apr 21 2011
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LINKS
| Robert G. Wilson v, Table of n, a(n) for n = 1..1000 . [From Robert G. Wilson v (rgwv(AT)rgwv.com), May 29 2009]
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MATHEMATICA
| nextPerfectPowers[n_] := Block[{k = n + 1}, While[GCD @@ Last /@ FactorInteger@ k == 1, k++ ]; k]; t = Table[0, {100}]; t[[3]] = 1; m = 0; While[m < 14400000, n = nextPerfectPowers@ m; d = n - m; If[d < 100 && t[[d]] == 0, t[[d]] = m; Print[{d, m}]]; m = n]; t [From Robert G. Wilson v (rgwv(AT)rgwv.com), May 29 2009]
(* checked against *) mx = 14400000; pp = Union[ Join[{1}, Flatten[ Table[n^i, {n, 2, Sqrt@mx}, {i, 2, Log[n, mx]}]]]]; d = Rest@ pp - Most@ pp; pp[[ # ]] & /@ Flatten[ Table[ Position[d, n, 1, 1], {n, 56}] /. {{} -> {0}}] /. {List -> 0} [From Robert G. Wilson v (rgwv(AT)rgwv.com), May 29 2009]
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CROSSREFS
| Cf. A189117 (conjectured number of pairs of consecutive perfect powers differing by n).
Sequence in context: A132586 A103953 A076444 * A103954 A200838 A122984
Adjacent sequences: A023053 A023054 A023055 * A023057 A023058 A023059
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KEYWORD
| nonn
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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