A129674 Permutation sequence generated by the "evil numbers" (A001969), by swapping n-th natural number by the (n-g)-th sequentially (iteratively), where g=min(evil(n+1)-evil(n)-1,n-1).

3, 2, 1, 6, 4, 7, 5, 10, 8, 12, 11, 13, 15, 14, 9, 18, 16, 20, 19, 21, 17, 24, 22, 25, 27, 26, 23, 30, 28, 31, 29, 34, 32, 36, 35, 37, 33, 40, 38, 41, 43, 42, 39, 46, 44, 48, 47, 49, 51, 50, 45, 54, 52, 55, 53, 58, 56, 60, 59, 61, 63, 62, 57, 66, 64, 68, 67, 69, 65, 72, 70, 73

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 (apart from the initial cycle of length 2). It is also notable that the difference of the number of fixed points and the number of cycles never differs by more than 4, 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

Index entries for sequences that are permutations of the natural numbers

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(A001969)

Crossrefs

Inverse of A129675, Cf. A128754, A128756, A129676, A129677, A129678 and A001969.

Sequence in context: A031252 A208152 A194761 * A120771 A115094 A165958

Adjacent sequences: A129671 A129672 A129673 * A129675 A129676 A129677

Keyword

nonn,base

Author

Ferenc Adorjan (fadorjan(AT)freemail.hu or ferencadorjan(AT)gmail.com), May 01 2007

Status

approved