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A336190 a(n) is the least k such that A336033(k) = n.

%I A336190 #12 Jul 14 2020 07:03:32
%S A336190 1,2,5,11,15,31,39,47,55,111,119,143,151,175,183,207,215,431,439,463,
%T A336190 471,559,567,591,599,687,695,719,727,815,823,847,855,1711,1719,1743,
%U A336190 1751,1839,1847,1871,1879,2223,2231,2255,2263,2351,2359,2383,2391,2735,2743
%N A336190 a(n) is the least k such that A336033(k) = n.
%C A336190 This sequence is strictly increasing.
%H A336190 Rémy Sigrist, <a href="/A336190/b336190.txt">Table of n, a(n) for n = 0..8192</a>
%H A336190 Rémy Sigrist, <a href="/A336190/a336190.txt">C program for A336190</a>
%F A336190 Apparently, a(2^(k+1)) = a(2^k) + A002066(k-1) for k > 0.
%e A336190 The first terms, alongside A336033, are:
%e A336190   n  a(n)  k   A336033(k)
%e A336190   -  ----  --  ----------
%e A336190   0     1   1           0
%e A336190   1     2   2           1
%e A336190             3           0
%e A336190             4           1
%e A336190   2     5   5           2
%e A336190             6           0
%e A336190             7           1
%e A336190             8           0
%e A336190             9           1
%e A336190            10           2
%e A336190   3    11  11           3
%e A336190            12           2
%e A336190            13           2
%e A336190            14           3
%e A336190   4    15  15           4
%o A336190 (PARI) { w=0; for (n=1, #a=vector(2743), x=0; forstep (k=n-1, 1, -1, if (!x=bitxor(x, a[k]), a[n]=1+a[k]; break)); if (w==a[n], print1 (n ", "); w++)) }
%o A336190 (C) See Links section.
%Y A336190 Cf. A002066, A336033.
%K A336190 nonn,base
%O A336190 0,2
%A A336190 _Rémy Sigrist_, Jul 11 2020