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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). 4
 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, 29, 28, 30, 26, 33, 31, 34, 36, 35, 32, 39, 37, 40, 38, 43, 41, 45, 44, 46, 48, 47, 42, 51, 49, 53, 52, 54, 50, 57, 55, 58, 60, 59, 56, 63, 61, 65, 64, 66, 68, 67, 62, 71, 69, 72, 70 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. LINKS Ferenc Adorjan, Table of n, a(n) for n = 1..10000 PROG (PARI) {vperm(z)=local(n, m, q, v, x, j, g); /* 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. */ 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); 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)} a=vperm(A000069) CROSSREFS Inverse of A129677, Cf. A128754, A128756, A129674, A129675, A129680 and A000069. Sequence in context: A112620 A325766 A021321 * A154947 A152747 A010847 Adjacent sequences:  A129673 A129674 A129675 * A129677 A129678 A129679 KEYWORD nonn,base AUTHOR Ferenc Adorjan (fadorjan(AT)freemail.hu or ferencadorjan(AT)gmail.com), May 01 2007 STATUS approved

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Last modified May 25 12:30 EDT 2019. Contains 323568 sequences. (Running on oeis4.)