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%I #5 Mar 07 2016 12:32:30
%S 1,2,3,4,5,6,11,8,7,9,31,10,127,18,13,14,709,12,5381,15,19,45,52711,
%T 16,17,165,23,27,648391,21,9737333,22,29,856,41,20,174440041,6185,61,
%U 24,3657500101,28,88362852307,63,43,58644,2428095424619,25,59,26,37,212,75063692618249,34,67,39,47
%N Permutation of natural numbers: a(1) = 1, a(2n) = A065090(1+a(n)), a(2n+1) = A000040(a(A268674(2n+1))).
%C Terms for prime positions copied from A007097.
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F a(1) = 1, a(2) = 2, for n > 2, if n is even, a(n) = A002808(a(n/2)-1), and for odd n, a(n) = A000040(a(A268674(n))).
%F As a composition of other permutations:
%F a(n) = A237739(A252756(n)).
%F Other identities. For all n >= 1:
%F a(A000040(n)) = A007097(n). [Maps primes to the primeth recurrence.]
%o (Scheme, with memoization-macro definec)
%o (definec (A269858 n) (cond ((<= n 1) n) ((even? n) (A065090 (+ 1 (A269858 (/ n 2))))) (else (A000040 (A269858 (A268674 n))))))
%Y Inverse: A269857.
%Y Cf. A000040, A007097, A065090, A268674.
%Y Related or similar permutations: A237739, A252756, A269848.
%K nonn
%O 1,2
%A _Antti Karttunen_, Mar 06 2016
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