A162945 Numbers k with squares that are concatenations k^2 = x//y such that x is an anagram of y.

836, 3911, 6926, 6941, 9701, 9786, 32119, 35268, 39011, 40104, 40645, 40991, 41489, 42849, 43204, 45743, 49498, 50405, 50705, 54335, 55493, 57089, 57111, 59872, 60406, 62043, 64396, 64671, 66979, 68595, 69028, 69907, 70107, 72475, 73625, 75926, 76279

Offset

1,1

Comments

Cases with leading zeros in y, for example 51674^2 = 2670202276, are not admitted.

Contains 4*10^(2*k)+10^k+4, 5*10^(2*k)+4*10^k+5, 5*10^(2*k)+7*10^k+5,

6*10^(2*k)+4*10^k+6, 7*10^(2*k)+10^k+7 for k >= 2. In particular, the sequence is infinite. - Robert Israel, Apr 16 2019

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Example

836^2 = 698896 = 698//896 and 698 is an anagram of 896.

Maple

isA162945 := proc(n) local n2, x, y ; n2 := convert(n^2, base, 10) ; if nops(n2) mod 2 = 0 then if op(nops(n2)/2, n2) <> 0 then y := sort( [op(1..nops(n2)/2, n2)] ); x := sort( [op(nops(n2)/2+1..nops(n2), n2)] ); RETURN( x = y) ; else false; fi; else false; fi; end:
for n from 1 to 90000 do if isA162945(n) then printf("%d, \n", n) ; fi; od: # R. J. Mathar, Jul 21 2009

Mathematica

Cases[If[OddQ@(l = IntegerLength@(p = #^2)),
    Nothing, {#, Partition[IntegerDigits@p, l/2]}] & /@
  Range@500000, {a_, _?(Sort@#[[1]] == Sort@#[[2]] && #[[2]][[1]] != 0 &)} :> a]  (* Hans Rudolf Widmer, Jul 19 2024 *)

Crossrefs

Sequence in context: A113856 A245947 A235288 * A138850 A357326 A322524

Adjacent sequences: A162942 A162943 A162944 * A162946 A162947 A162948

Keyword

nonn,base

Author

Claudio Meller, Jul 18 2009

Extensions

Keyword:base added by R. J. Mathar Jul 21 2009

Status

approved