

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 kth powers where neighboring digits are distinct (see A318763).  Robert Israel, Sep 03 2018


LINKS



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)):


CROSSREFS



KEYWORD

base,easy,nonn


AUTHOR



EXTENSIONS



STATUS

approved



