A128756 Permutation sequence related to lucky numbers A000959: starting with the integers, for n = 1, 2, 3, ... swap the n-th and the (n-g)-th element, where g = A000959(n+1) - A000959(n) - 1.

6, 3, 14, 7, 2, 11, 12, 9, 1, 5, 4, 15, 20, 17, 26, 21, 22, 23, 36, 10, 19, 31, 8, 13, 32, 27, 16, 29, 34, 33, 48, 30, 28, 39, 42, 41, 44, 35, 37, 43, 24, 45, 52, 47, 50, 51, 58, 55, 25, 67, 56, 53, 38, 63, 62, 54, 64, 61, 40, 77, 66, 71, 68, 18, 70, 59, 78, 79, 74, 85, 65, 46

Offset: 1

Author

Ferenc Adorjan (fadorjan(AT)freemail.hu or ferencadorjan(AT)gmail.com), Mar 24 2007

Keywords

• nonn

Comments

Similarly to A128754, this sequence also shows the characteristics of an "infinite braid".

Links

• Ferenc Adorjan, Table of n,a(n) for n=1..10000
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse of A128757. Cf. A128754, A128755 and A000959.

Programs

PARI

{vperm(z)=local(n,j,g); /* Permutation of positive integers: starting with the sequence of positive integers, for i = 1, 2, 3,..., swap the i-th term with max(i-g(i),1)-th term, where g(i) = z[i+1]-z[i]-1. */
  j=length(z)-1; n=j-z[j]+z[j-6]; v=[1..j];
  for(i=1,j, g=min(z[i+1]-z[i]-1,i-1); [v[i],v[i-g]]=[v[i-g],v[i]]);
  return(v[1..n])}
a=vperm(A000959_upto(10^3))

Extensions

Edited by M. F. Hasler, Jan 09 2020