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 A090516 Perfect powers (at least a square) in which neighboring digits are distinct. 4
 1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 81, 121, 125, 128, 169, 196, 216, 243, 256, 289, 324, 343, 361, 484, 512, 529, 576, 625, 676, 729, 784, 841, 961, 1024, 1089, 1296, 1369, 1521, 1681, 1728, 1764, 1849, 1936, 2025, 2048, 2187, 2197, 2304, 2401, 2601 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Sequence must be infinite but a proof is needed. Subsidiary sequences; Perfect squares or perfect cubes etc. in which neighboring digits are distinct. On the other hand, for k >= 22 we might expect only finitely many k-th powers where neighboring digits are distinct (see A318763). - Robert Israel, Sep 03 2018 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 MAPLE N:= 5000: filter:= proc(n) local L; L:= convert(n, base, 10); not member(0, L[2..-1]-L[1..-2]) end proc: P:= sort(convert({seq(seq(i^k, i=1..floor(N^(1/k))), k=2..ilog2(N))}, list)): select(filter, P); # Robert Israel, Sep 03 2018 CROSSREFS Cf. A001597 (perfect powers), A075309 (distinct-digit perfect powers), A318763. Sequence in context: A359493 A072777 A076292 * A090515 A075309 A175031 Adjacent sequences: A090513 A090514 A090515 * A090517 A090518 A090519 KEYWORD base,easy,nonn AUTHOR Amarnath Murthy, Dec 06 2003 EXTENSIONS Corrected and extended by Rick L. Shepherd, Jul 01 2005 Offset corrected by Robert Israel, Sep 03 2018 STATUS approved

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Last modified July 15 21:59 EDT 2024. Contains 374334 sequences. (Running on oeis4.)