A061658 Numbers k > 1 such that, in base 4, k and k^2 contain the same digits in the same proportion.

45, 165, 180, 657, 660, 720, 882, 2165, 2193, 2331, 2625, 2628, 2640, 2880, 3362, 3470, 3528, 3606, 3683, 3825, 8285, 8294, 8337, 8381, 8477, 8493, 8519, 8525, 8660, 8721, 8772, 8817, 9069, 9282, 9324, 9479, 9507, 9869, 9969, 10185, 10349, 10353, 10500, 10512

Offset: 1

Author

Erich Friedman, Jun 16 2001

Keywords

• base
• easy
• nonn

Examples

			45 = 231_4 and 45^2 = 133221_4.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A061656, A061657, A061659, A061660, A061661, A061662, A061663, A114258, A061664.

Programs

Maple

p:= n-> add(x^i, i=convert(n, base, 4)):
a:= proc(n) option remember; local k;
      for k from 1+`if`(n=1, 0, a(n-1))
      while p(k)*2<>p(k^2) do od; k
    end:
seq(a(n), n=1..50);  # Alois P. Heinz, May 10 2015

Extensions

Offset changed to 1 by Alois P. Heinz, May 10 2015