

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
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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 kth 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 (distinctdigit perfect powers), A318763.
Sequence in context: A001597 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



