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A366264 Inverse of A366263, where A366263 is the Doudna sequence permuted by Blue code.

%I A366264 #10 Oct 06 2023 14:14:27
%S A366264 0,1,3,2,5,4,15,7,6,14,17,13,51,16,12,8,85,11,255,19,18,50,257,22,10,
%T A366264 84,9,49,771,21,1285,25,48,254,20,28,3855,256,86,52,4369,55,13107,87,
%U A366264 23,770,21845,59,30,31,252,253,65535,26,54,82,258,1284,65537,62,196611,3854,53,42,80,81,327685,259,768,61,983055
%N A366264 Inverse of A366263, where A366263 is the Doudna sequence permuted by Blue code.
%H A366264 Antti Karttunen, <a href="/A366264/b366264.txt">Table of n, a(n) for n = 1..8192</a>
%H A366264 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%H A366264 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A366264 a(n) = A193231(A156552(n)).
%F A366264 For all n >= 0, a(A366263(n)) = n, and for all n >= 1, A366263(a(n)) = n.
%F A366264 For all n >= 2, 1+A268389(a(n)) = A055396(n).
%o A366264 (PARI)
%o A366264 A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
%o A366264 A193231(n) = { my(x='x); subst(lift(Mod(1, 2)*subst(Pol(binary(n), x), x, 1+x)), x, 2) };
%o A366264 A366264(n) = A193231(A156552(n));
%Y A366264 Cf. A156552, A193231, A366263 (inverse map).
%Y A366264 Cf. A055396, A268389.
%K A366264 nonn
%O A366264 1,3
%A A366264 _Antti Karttunen_, Oct 06 2023