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A145342 a(n) = (A145341(n) + 1)/2.

%I A145342 #36 Apr 09 2019 05:10:08
%S A145342 1,2,3,4,5,7,6,8,9,13,11,15,10,14,12,16,17,25,21,29,19,27,23,31,18,26,
%T A145342 22,30,20,28,24,32,33,49,41,57,37,53,45,61,35,51,43,59,39,55,47,63,34,
%U A145342 50,42,58,38,54,46,62,36,52,44,60,40,56,48,64,65,97,81,113,73,105,89
%N A145342 a(n) = (A145341(n) + 1)/2.
%C A145342 This sequence is a permutation of the positive integers. It is its own inverse permutation.
%C A145342 Fixed points of the permutation are the terms of A044051. - _Ivan Neretin_, Oct 31 2015
%C A145342 From _Yosu Yurramendi_, Feb 04 2019: (Start)
%C A145342 If the terms (n > 0) are written as an array (left-aligned fashion) with rows of length 2^m, m = 0,1,2,3,...
%C A145342    1;
%C A145342    2,  3;
%C A145342    4,  5,  7,  6;
%C A145342    8,  9, 13, 11, 15, 10, 14, 12;
%C A145342   16, 17, 25, 21, 29, 19, 27, 23, 31, 18, 26, 22, 30, 20, 28, 24;
%C A145342   32, 33, 49, 41, 57, 37, 53, 45, 61, 35, 51, 43, 59, 39, 55, 47, 63, 34, ...
%C A145342 then the following relationship can be observed:
%C A145342 a(1) = 1, a(2) = 2, a(3) = 3,
%C A145342 for m > 0, a(2^(m+1)) = 2*a(2^m), a(2^m + 1) = a(2^m) + 1, a(2^(m+1)+ 2^m) = 2*a(2^(m+1)) - 1, for 0 < k < 2^m, a(2^(m+1)+ k) = 2*a(2^m + k) - 1, a(2^(m+1)+ 2^m + k) = a(2^(m+1) + k) + 1
%C A145342 (End)
%H A145342 Ivan Neretin, <a href="/A145342/b145342.txt">Table of n, a(n) for n = 1..8192</a>
%H A145342 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%t A145342 Table[(FromDigits[Reverse[IntegerDigits[2n-1, 2]], 2] +1)/2, {n, 71}] (* _Ivan Neretin_, Oct 31 2015 *)
%o A145342 (R)
%o A145342 nmax <- 10^3 # by choice
%o A145342 b <- vector()
%o A145342 for (o in seq(1,nmax,2)){
%o A145342   w <- which(as.numeric(intToBits(o))==1)
%o A145342   b <- c(b, sum(2^(max(w)-w)))
%o A145342 }
%o A145342 a <- (b+1)/2
%o A145342 a[1:71]
%o A145342 # _Yosu Yurramendi_, Feb 04 2019
%o A145342 (PARI) a(n) = (1+fromdigits(Vecrev(binary(2*n-1)), 2))/2; \\ _Michel Marcus_, Feb 04 2019
%Y A145342 Cf. A044051, A145341.
%K A145342 base,nonn
%O A145342 1,2
%A A145342 _Leroy Quet_, Oct 08 2008
%E A145342 More terms from _R. J. Mathar_ and _Ray Chandler_, Oct 10 2008