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Permutation of natural numbers: a(1) = 0, after which, a(2n) = A087686(1+a(n)), a(2n+1) = A088359(a(A268674(2n+1))).
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%I #7 Mar 07 2016 12:31:54

%S 0,1,3,2,6,7,11,4,5,14,20,15,37,26,13,8,70,12,135,30,9,47,264,31,10,

%T 85,25,57,521,29,1034,16,28,156,23,27,2059,292,46,62,4108,21,8205,105,

%U 17,557,16398,63,19,24,22,191,32783,56,18,120,55,1079,65552,61,131089,2114,84,32,44,60,262162,348,59,53

%N Permutation of natural numbers: a(1) = 0, after which, a(2n) = A087686(1+a(n)), a(2n+1) = A088359(a(A268674(2n+1))).

%C Note the indexing: Domain starts from 1, range from 0.

%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>

%H <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>

%F a(1) = 0; after which, for even n, a(n) = A087686(1+a(n/2)), and for odd n, a(n) = A088359(a(A268674(n))).

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

%F a(2^n) = 2^(n-1).

%F As a composition of other permutations:

%F a(n) = A267112(A252756(n)).

%o (Scheme, with memoization-macro definec)

%o (definec (A269852 n) (cond ((= n 1) 0) ((even? n) (A087686 (+ 1 (A269852 (/ n 2))))) (else (A088359 (A269852 (A268674 n))))))

%Y Inverse: A269851.

%Y Cf. A004001, A087686, A088359, A268674.

%Y Related or similar permutations: A252756, A267112, A269856.

%K nonn

%O 1,3

%A _Antti Karttunen_, Mar 07 2016