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Permutation of natural numbers: a(1) = 1, a(2n) = A000079(A055396(2n+1)-1) * ((2*A246277(2n+1))-1), a(2n+1) = 1 + 2*a(n).
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%I #9 Sep 11 2014 18:56:40

%S 1,2,3,4,5,8,7,6,9,16,11,32,17,10,15,64,13,128,19,18,33,256,23,12,65,

%T 14,35,512,21,1024,31,26,129,20,27,2048,257,42,39,4096,37,8192,67,22,

%U 513,16384,47,24,25,50,131,32768,29,36,71,66,1025,65536,43,131072,2049,38,63,52,53,262144,259,74,41

%N Permutation of natural numbers: a(1) = 1, a(2n) = A000079(A055396(2n+1)-1) * ((2*A246277(2n+1))-1), a(2n+1) = 1 + 2*a(n).

%C See the comments in A246675. This is otherwise similar permutation, except for odd numbers, which are here recursively permuted by the emerging permutation itself. The even bisection halved gives A246679, the odd bisection from a(3) onward with one subtracted and then halved gives this sequence back.

%H Antti Karttunen, <a href="/A246677/b246677.txt">Table of n, a(n) for n = 1..2048</a>

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

%F a(1) = 1, a(2n) = A000079(A055396(2n+1)-1) * ((2*A246277(2n+1))-1), a(2n+1) = 1 + 2*a(n).

%o (Scheme, with memoization-macro definec)

%o (definec (A246677 n) (cond ((<= n 1) n) ((odd? n) (+ 1 (* 2 (A246677 (/ (- n 1) 2))))) (else (* (A000079 (- (A055396 (+ 1 n)) 1)) (-1+ (* 2 (A246277 (+ 1 n))))))))

%Y Inverse: A246678. Variants: A246675, A246683.

%Y Even bisection halved: A246679.

%Y Cf. A000079, A055396, A246277.

%Y a(n) differs from A156552(n+1) for the first time at n=32, where a(32) = 26, while A156552(33) = 34.

%K nonn

%O 1,2

%A _Antti Karttunen_, Sep 01 2014