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%I #14 Jul 30 2014 08:58:07
%S 1,2,3,4,5,6,9,10,7,8,13,18,17,26,11,12,37,34,25,74,15,16,69,50,21,14,
%T 19,20,33,138,41,66,35,52,53,22,277,82,31,32,45,554,65,90,27,36,1109,
%U 130,101,42,43,28,73,2218,149,30,71,104,57,146,209,114,51,148,133,70,293,418,555,164,141,586,329,282,75,68,105,106,1173,658,23,24
%N Permutation of natural numbers: a(1) = 1, a(2n) = 2 * a(A064989(2n-1)), a(2n-1) = 1 + (2 * a(A064989(2n-1)-1)).
%C The even bisection halved gives A245607. The odd bisection incremented by one and halved gives A245707.
%H Antti Karttunen, <a href="/A245605/b245605.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) = 2 * a(A064989(2n-1)), a(2n-1) = 1 + (2 * a(A064989(2n-1)-1)).
%F a(1) = 1, a(2n) = 2 * a(A064216(n)), a(2n-1) = 1 + (2 * a(A064216(n)-1)).
%F As a composition of related permutations:
%F a(n) = A245607(A048673(n)).
%o (PARI)
%o A064989(n) = my(f = factor(n)); for(i=1, #f~, if((2 == f[i,1]),f[i,1] = 1,f[i,1] = precprime(f[i,1]-1))); factorback(f);
%o A245605(n) = if(1==n, 1, if(0==(n%2), 2*A245605(A064989(n-1)), 1+(2*A245605(A064989(n)-1))));
%o for(n=1, 10001, write("b245605.txt", n, " ", A245605(n)));
%o (Scheme, with memoization-macro definec)
%o (definec (A245605 n) (cond ((= 1 n) 1) ((even? n) (* 2 (A245605 (A064989 (- n 1))))) (else (+ 1 (* 2 (A245605 (-1+ (A064989 n))))))))
%Y Inverse: A245606.
%Y Cf. A048673, A064216, A064989, A245607, A245705, A245707.
%Y Similar entanglement permutations: A244319, A005940, A163511, A243287, A243343, A243345, A244321, A245603, A245613, A135141, A237427.
%K nonn
%O 1,2
%A _Antti Karttunen_, Jul 29 2014
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