A161861 Cubes which are anagrams of squares.

1, 64, 729, 1000, 2197, 4096, 9261, 15625, 19683, 21952, 46656, 64000, 91125, 110592, 117649, 132651, 157464, 216000, 226981, 262144, 328509, 343000, 373248, 531441, 592704, 614125, 681472, 729000, 884736, 912673, 1000000, 1061208, 1157625

Offset

1,2

Comments

If k is present then so is 1000k.

Cube root of n's: 1, 4, 9, 10, 13, 16, 21, 25, 27, 28, 36, 40, 45, 48, 49, 51, 54, 60, 61, 64, ..., .

Leading zeros in squares are allowed, i.e. an anagram of 1000 is 0001. - Chai Wah Wu, Nov 04 2016

Links

Robert G. Wilson v and Chai Wah Wu, Table of n, a(n) for n = 1..10000 a(n) for n = 1..872 from Robert G. Wilson v.

Example

2197 is a term because it is a cube (13^3) and 7921 (an anagram of 2197) is a square (89 * 89).

Mathematica

fQ[n_] := Union[ IntegerQ@ Sqrt@ FromDigits@ # & /@ Permutations@ IntegerDigits@ n][[-1]] == True; lst = {}; Do[ If[ fQ[n^3], AppendTo[lst, n^3]; Print[n^3]], {n, 1650}] (* Or for larger n's *)
(* first do *) Needs[ "Combinatorica`" ] (* then *) fQ[ n_ ] := Block[ {id = IntegerDigits@n, k = 1, mx = Floor[ Log[ 10, n ] +1 ]! +1}, While[ k < mx && !IntegerQ@ Sqrt@ FromDigits@ UnrankPermutation[ k, id ], k++ ]; If[ k != mx, True, False ] ]

Crossrefs

Includes A001014.

Sequence in context: A351194 A048392 A274219 * A179149 A074471 A164345

Adjacent sequences: A161858 A161859 A161860 * A161862 A161863 A161864

Keyword

nonn,base

Author

Claudio Meller, Jun 20 2009

Extensions

Edited, corrected, extended by Robert G. Wilson v, Jun 30 2009

Status

approved