[go: up one dir, main page]

login
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
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
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
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