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%I
%S 1,2,3,4,5,6,9,10,7,8,15,16,11,26,21,22,13,12,27,28,25,36,81,82,19,14,
%T 45,52,125,56,39,40,29,18,33,46,17,126,99,100,31,50,51,226,41,626,129,
%U 130,89,24,63,34,35,176,87,154,59,344,825,298,115,86,189,190,43,32,105,76,23,66,57,88,53,20
%N Permutation of natural numbers: a(1) = 1, a(2n) = 1 + A003961(a(n)), a(2n+1) = A003961(1+a(n)). [Where A003961(n) shifts the prime factorization of n one step left].
%C The even bisection halved gives A245608. The odd bisection incremented by one and halved gives A245708.
%H Antti Karttunen, <a href="/A245606/b245606.txt">Table of n, a(n) for n = 1..10001</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) = A243501(a(n)), a(2n+1) = A003961(1+a(n)).
%F As a composition of related permutations:
%F a(n) = A064216(A245608(n)).
%o (PARI)
%o A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ This function from _Michel Marcus_
%o A245606(n) = if(1==n,1,if(0==(n%2),1+A003961(A245606(n/2)),A003961(1+A245606((n-1)/2))))
%o for(n=1, 10001, write("b245606.txt", n, " ", A245606(n)))
%o (Scheme, with memoization-macro definec)
%o (definec (A245606 n) (cond ((= 1 n) 1) ((even? n) (A243501 (A245606 (/ n 2)))) (else (A003961 (+ 1 (A245606 (/ (- n 1) 2)))))))
%Y Inverse: A245605.
%Y Cf. A003961, A243501, A064216, A245608, A245706, A245708.
%Y Similar entanglement permutations: A244319, A156552, A243071, A243288, A243344, A243346, A244322, A245604, A245614, A227413, A237126.
%K nonn
%O 1,2
%A _Antti Karttunen_, Jul 29 2014
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