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A243065 Permutation of natural numbers, the odd bisection of A241909 halved; equally, a composition of A064216 and A241909: a(n) = A241909(A064216(n)).

%I A243065 #21 Jun 21 2014 14:16:03
%S A243065 1,2,4,8,3,16,32,9,64,128,27,256,6,5,512,1024,81,18,2048,243,4096,
%T A243065 8192,25,16384,12,729,32768,54,2187,65536,131072,125,162,262144,6561,
%U A243065 524288,1048576,15,36,2097152,7,4194304,486,19683,8388608,108,59049,1458,16777216,625,33554432,67108864,75
%N A243065 Permutation of natural numbers, the odd bisection of A241909 halved; equally, a composition of A064216 and A241909: a(n) = A241909(A064216(n)).
%C A243065 Are there any other fixed points than 1, 2, 18 and 72?
%H A243065 Antti Karttunen, <a href="/A243065/b243065.txt">Table of n, a(n) for n = 1..512</a>
%H A243065 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A243065 a(1) = 1, and for n>=2, a(n) = A241909(2n-1)/2. Equally, a(n) = ceiling(A241909(2n-1)/2) for all n.
%F A243065 As a composition of related permutations:
%F A243065 a(n) = A241909(A064216(n)).
%F A243065 a(n) = A241909(A243061(A241909(n))).
%F A243065 For all n, a(A006254(n)) = 2^n.
%o A243065 (Scheme) (define (A243065 n) (A241909 (A064216 n)))
%Y A243065 Inverse: A243066.
%Y A243065 Cf. A064216, A241909, A243505-A243506, A244152-A244154, A243061-A243062, A006254.
%K A243065 nonn
%O A243065 1,2
%A A243065 _Antti Karttunen_, Jun 01 2014