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A276441 Permutation of natural numbers: a(1) = 1, a(A087686(1+n)) = 1 + 2*a(n), a(A088359(n)) = 2*a(n), where A088359 & A087686 = numbers that occur only once & more than once in A004001.

%I A276441 #12 Sep 03 2016 17:04:38
%S A276441 1,3,2,7,6,4,5,15,14,12,8,13,10,9,11,31,30,28,24,16,29,26,20,25,18,17,
%T A276441 27,22,21,19,23,63,62,60,56,48,32,61,58,52,40,57,50,36,49,34,33,59,54,
%U A276441 44,53,42,41,51,38,37,35,55,46,45,43,39,47,127,126,124,120,112,96,64,125,122,116,104,80,121,114,100,72,113,98
%N A276441 Permutation of natural numbers: a(1) = 1, a(A087686(1+n)) = 1 + 2*a(n), a(A088359(n)) = 2*a(n), where A088359 & A087686 = numbers that occur only once & more than once in A004001.
%H A276441 Antti Karttunen, <a href="/A276441/b276441.txt">Table of n, a(n) for n = 1..8191</a>
%H A276441 T. Kubo and R. Vakil, <a href="http://dx.doi.org/10.1016/0012-365X(94)00303-Z">On Conway's recursive sequence</a>, Discr. Math. 152 (1996), 225-252.
%H A276441 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A276441 <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>
%H A276441 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A276441 a(1) = 1; for n > 1, if A093879(n-1) = 0 [when n is in A087686], a(n) = 1 + 2*a(A080677(n)-1), otherwise [when n is in A088359], a(n) = 2*a(A004001(n)-1).
%F A276441 As a composition of other permutations:
%F A276441 a(n) = A054429(A267111(n)).
%F A276441 a(n) = A233277(A276343(n)).
%F A276441 a(n) = A233275(A276345(n)).
%F A276441 a(n) = A006068(A276443(n)).
%F A276441 Other identities. For all n >= 1:
%F A276441 a(A000079(n-1)) = A000225(n).
%o A276441 (Scheme)
%o A276441 (definec (A276441 n) (cond ((< n 2) n) ((zero? (A093879 (- n 1))) (+ 1 (* 2 (A276441 (+ -1 (A080677 n)))))) (else (* 2 (A276441 (+ -1 (A004001 n)))))))
%Y A276441 Inverse: A276442.
%Y A276441 Cf. A000079, A000225, A004001, A080677, A087686, A088359, A093879.
%Y A276441 Related or similar permutations: A006068, A054429, A233275, A233277, A267111, A276343, A276345, A276443.
%Y A276441 Cf. also arrays A265901, A265903.
%K A276441 nonn,base
%O A276441 1,2
%A A276441 _Antti Karttunen_, Sep 03 2016