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A243066 Permutation of natural numbers, the even bisection of A241909 incremented by one and halved; equally, a composition of A241909 and A048673: a(n) = A048673(A241909(n)).

%I A243066 #19 Jun 21 2014 14:16:20
%S A243066 1,2,5,3,14,13,41,4,8,63,122,25,365,313,38,6,1094,18,3281,172,188,
%T A243066 1563,9842,61,23,7813,11,1201,29525,123,88574,7,938,39063,113,39,
%U A243066 265721,195313,4688,666,797162,858,2391485,8404,74,976563,7174454,85,68,88,23438,58825,21523361,28
%N A243066 Permutation of natural numbers, the even bisection of A241909 incremented by one and halved; equally, a composition of A241909 and A048673: a(n) = A048673(A241909(n)).
%C A243066 For n > 1, 2n is found in A241909 from the position (2*a(n))-1. I.e., A241909((2*a(n))-1) = 2n for all n >= 2.
%C A243066 Or in other words, a(n) gives the position in the odd bisection of A241909 where 2n is located at.
%C A243066 Are there any other fixed points than 1, 2, 18 and 72?
%H A243066 Antti Karttunen, <a href="/A243066/b243066.txt">Table of n, a(n) for n = 1..512</a>
%H A243066 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A243066 a(1) = 1, a(n) = (A241909(2*n)+1)/2.
%F A243066 As a composition of related permutations:
%F A243066 a(n) = A048673(A241909(n)).
%F A243066 a(n) = A241909(A243062(A241909(n))).
%F A243066 For all n>=1, a(2^n) = A006254(n).
%o A243066 (Scheme, two alternatives)
%o A243066 (define (A243066 n) (if (= n 1) 1 (/ (+ 1 (A241909 (* 2 n))) 2)))
%o A243066 (define (A243066 n) (A048673 (A241909 n)))
%Y A243066 Inverse: A243065.
%Y A243066 Cf. A048673, A241909, A243505-A243506, A244152-A244154, A243061-A243062.
%K A243066 nonn
%O A243066 1,2
%A A243066 _Antti Karttunen_, Jun 01 2014