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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.
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%I #12 Sep 03 2016 17:04:38

%S 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 27,22,21,19,23,63,62,60,56,48,32,61,58,52,40,57,50,36,49,34,33,59,54,

%U 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 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 Antti Karttunen, <a href="/A276441/b276441.txt">Table of n, a(n) for n = 1..8191</a>

%H 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 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%H <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F 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 As a composition of other permutations:

%F a(n) = A054429(A267111(n)).

%F a(n) = A233277(A276343(n)).

%F a(n) = A233275(A276345(n)).

%F a(n) = A006068(A276443(n)).

%F Other identities. For all n >= 1:

%F a(A000079(n-1)) = A000225(n).

%o (Scheme)

%o (definec (A276441 n) (cond ((< n 2) n) ((zero? (A093879 (- n 1))) (+ 1 (* 2 (A276441 (+ -1 (A080677 n)))))) (else (* 2 (A276441 (+ -1 (A004001 n)))))))

%Y Inverse: A276442.

%Y Cf. A000079, A000225, A004001, A080677, A087686, A088359, A093879.

%Y Related or similar permutations: A006068, A054429, A233275, A233277, A267111, A276343, A276345, A276443.

%Y Cf. also arrays A265901, A265903.

%K nonn,base

%O 1,2

%A _Antti Karttunen_, Sep 03 2016