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A129676 Permutation sequence generated by the "odious numbers" (A000069), by swapping n-th natural number by the (n-g)-th sequentially, where g=min(odious(n+1)-odious(n)-1,n-1).

%I A129676 #9 Apr 12 2018 08:29:35
%S A129676 3,1,5,4,6,2,9,7,10,12,11,8,15,13,17,16,18,20,19,14,23,21,24,22,27,25,
%T A129676 29,28,30,26,33,31,34,36,35,32,39,37,40,38,43,41,45,44,46,48,47,42,51,
%U A129676 49,53,52,54,50,57,55,58,60,59,56,63,61,65,64,66,68,67,62,71,69,72,70
%N A129676 Permutation sequence generated by the "odious numbers" (A000069), by swapping n-th natural number by the (n-g)-th sequentially, where g=min(odious(n+1)-odious(n)-1,n-1).
%C A129676 In contrast to A128754 and A128756 (which are generated analogously from the primes and the lucky numbers, respectively), this sequence seems consisting solely of fixed points and cycles of length 4,5 and 6. It is also notable that the difference of the number of fixed points and the number of cycles never differs by more than 3, up to index 10000, according to numerical tests. Thus the ratio of the number of fixed points to the number of cycles seems to be asymptotically equal to unity.
%H A129676 Ferenc Adorjan, <a href="/A129676/b129676.txt">Table of n, a(n) for n = 1..10000</a>
%H A129676 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%o A129676 (PARI) {vperm(z)=local(n,m,q,v,x,j,g);
%o A129676 /* Permutation of positive integers so that starting with the sequence of positive integers, sequentially swap the i-th term with max(i-g(i),1)-th term, where g(i)=z[i+1]-z[i]-1. */
%o A129676 j=matsize(z)[2]-1;n=j-z[j]+z[j-6];v=vector(j);x=vector(n);for(i=1,j,v[i]=i);
%o A129676 for(i=1,j,g=min(z[i+1]-z[i]-1,i-1);q=v[i];v[i]=v[i-g];v[i-g]=q);for(i=1,n,x[i]=v[i]);return(x)}
%o A129676 a=vperm(A000069)
%Y A129676 Inverse of A129677, Cf. A128754, A128756, A129674, A129675, A129680 and A000069.
%K A129676 nonn,base
%O A129676 1,1
%A A129676 Ferenc Adorjan (fadorjan(AT)freemail.hu or ferencadorjan(AT)gmail.com), May 01 2007