This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A352783 #9 Apr 04 2022 10:20:38
%S A352783 0,1,2,5,3,9,10,21,4,13,18,37,11,41,42,85,6,17,26,53,19,73,74,149,20,
%T A352783 45,82,165,43,169,170,341,7,25,34,69,27,105,106,213,36,77,146,293,75,
%U A352783 297,298,597,22,81,90,181,83,329,330,661,84,173,338,677,171,681
%N A352783 Inverse permutation to A352782.
%H A352783 Rémy Sigrist, <a href="/A352783/b352783.txt">Table of n, a(n) for n = 0..8192</a>
%H A352783 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A352783 A069010(a(n)) = A000120(n).
%F A352783 a(2^k) = A023758(k+1) for any k >= 0.
%e A352783 A352782(42) = 14, so a(14) = 42.
%o A352783 (PARI) a(n) = { my (v=0, s=1, e, oz, o); while (n, n\=2^e=1+valuation(n, 2); oz = (sqrtint(e*8)+1)\2; o = e-binomial((sqrtint(8*e)+1)\2, 2); v += s * (2^o-1) * 2^(oz-o); s *= 2^(1+oz)); v }
%Y A352783 Cf. A000120, A069010, A352782.
%K A352783 nonn,base
%O A352783 0,3
%A A352783 _Rémy Sigrist_, Apr 02 2022