login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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