A258411 Nonnegative integers n such that in bijective base-2 numeration the number of occurrences of each digit doubles when n is squared.

5, 9, 17, 33, 41, 42, 65, 74, 77, 84, 85, 90, 129, 138, 145, 146, 148, 162, 166, 168, 173, 180, 257, 266, 274, 276, 279, 282, 285, 292, 296, 297, 301, 307, 310, 322, 324, 330, 332, 336, 341, 345, 349, 354, 360, 513, 522, 530, 532, 538, 545, 546, 548, 552, 562

Offset: 1

Author

Alois P. Heinz, May 29 2015

Keywords

• nonn
• base

Examples

			5 = 21_bij2 and 5^2 = 25 = 2121_bij2, 42 = 12122_bij2 and 42^2 = 1764 = 2122211212_bij2.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• Wikipedia, Bijective numeration

Crossrefs

Cf. A007931, A214676, A257867, A258410.

Programs

Maple

p:= proc(n) local d, m, r; m:= n; r:= 0;
      while m>0 do d:= irem(m, 2, 'm');
        if d=0 then d:=2; m:= m-1 fi;
        r:= r+x^d
      od; r
    end:
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..60);