login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons 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

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: 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

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 20 07:41 EST 2020. Contains 332069 sequences. (Running on oeis4.)