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A023056 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. 6
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; text; internal format)
OFFSET

1,1

COMMENTS

Searching up to 10^22, the largest term for n <= 1000 is a(618) = 421351^3 = 74805251419106551. - T. D. Noe, Apr 21 2011

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..10000

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 (* Robert G. Wilson v, 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} (* Robert G. Wilson v, May 29 2009 *)

CROSSREFS

Cf. A189117 (conjectured number of pairs of consecutive perfect powers differing by n).

Cf. A103954. (the powerful (A001694) analogous sequence).

Sequence in context: A208400 A103953 A076444 * A103954 A217012 A200838

Adjacent sequences:  A023053 A023054 A023055 * A023057 A023058 A023059

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified October 23 09:28 EDT 2019. Contains 328345 sequences. (Running on oeis4.)