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

%I A258411 #8 Feb 06 2017 14:38:17
%S A258411 5,9,17,33,41,42,65,74,77,84,85,90,129,138,145,146,148,162,166,168,
%T A258411 173,180,257,266,274,276,279,282,285,292,296,297,301,307,310,322,324,
%U A258411 330,332,336,341,345,349,354,360,513,522,530,532,538,545,546,548,552,562
%N A258411 Nonnegative integers n such that in bijective base-2 numeration the number of occurrences of each digit doubles when n is squared.
%H A258411 Alois P. Heinz, <a href="/A258411/b258411.txt">Table of n, a(n) for n = 1..10000</a>
%H A258411 Wikipedia, <a href="https://en.wikipedia.org/wiki/Bijective_numeration">Bijective numeration</a>
%e A258411 5 = 21_bij2 and 5^2 = 25 = 2121_bij2, 42 = 12122_bij2 and 42^2 = 1764 = 2122211212_bij2.
%p A258411 p:= proc(n) local d, m, r; m:= n; r:= 0;
%p A258411       while m>0 do d:= irem(m, 2, 'm');
%p A258411         if d=0 then d:=2; m:= m-1 fi;
%p A258411         r:= r+x^d
%p A258411       od; r
%p A258411     end:
%p A258411 a:= proc(n) option remember; local k;
%p A258411       for k from 1+`if`(n=1, 0, a(n-1))
%p A258411       while p(k)*2<>p(k^2) do od; k
%p A258411     end:
%p A258411 seq(a(n), n=1..60);
%Y A258411 Cf. A007931, A214676, A257867, A258410.
%K A258411 nonn,base
%O A258411 1,1
%A A258411 _Alois P. Heinz_, May 29 2015