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A255565 a(0) = 0; for n >= 1: if n = A255411(k) for some k, then a(n) = 2*a(k), otherwise, n = A256450(h) for some h, and a(n) = 1 + 2*a(h).

%I A255565 #21 May 30 2016 18:22:50
%S A255565 0,1,3,7,2,15,5,31,11,63,23,127,6,47,255,13,14,95,4,511,27,29,30,191,
%T A255565 9,1023,55,59,61,383,19,2047,111,119,123,767,39,4095,223,239,247,1535,
%U A255565 79,8191,447,479,495,3071,10,159,16383,895,62,959,991,6143,21,319,32767,1791,22,125,1919,1983,126,12287,46,43,639,65535,254,3583,12
%N A255565 a(0) = 0; for n >= 1: if n = A255411(k) for some k, then a(n) = 2*a(k), otherwise, n = A256450(h) for some h, and a(n) = 1 + 2*a(h).
%C A255565 Because all terms of A255411 are even it means that even terms can only occur in even positions (together with some odd terms, for each one of which there is a separate infinite cycle), while terms in odd positions are all odd.
%H A255565 Antti Karttunen, <a href="/A255565/b255565.txt">Table of n, a(n) for n = 0..5040</a>
%H A255565 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%H A255565 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A255565 a(0) = 0; for n >= 1: if A257680(n) = 0 [i.e., n is one of the terms of A255411], then a(n) = 2*a(A257685(n)), otherwise [when n is one of the terms of A256450], a(n) = 1 + 2*a(A273662(n)).
%F A255565 Other identities:
%F A255565 For all n >= 1, A001511(a(n)) = A257679(n).
%F A255565 For all n >= 1, a(A001563(n)) = A000079(n-1) = 2^(n-1).
%F A255565 For all n >= 1, a(A000142(n)) = A083318(n-1).
%o A255565 (Scheme, with memoization-macro definec)
%o A255565 (definec (A255565 n) (cond ((zero? n) n) ((zero? (A257680 n)) (* 2 (A255565 (A257685 n)))) (else (+ 1 (* 2 (A255565 (A273662 n)))))))
%Y A255565 Inverse: A255566.
%Y A255565 Cf. A000079, A000142, A001511, A001563, A083318, A255411, A256450, A257679, A257680, A257682, A257685.
%Y A255565 Cf. also arrays A257503, A257505.
%Y A255565 Related or similar permutations: A273665, A273668.
%K A255565 nonn,base
%O A255565 0,3
%A A255565 _Antti Karttunen_, May 05 2015
%E A255565 Formula changed because of the changed starting offset of A256450 - _Antti Karttunen_, May 30 2016