A128754 Permutation of positive integers obtained by swapping n-th natural number with the (n-g)-th sequentially, where g=prime(n+1)-prime(n)-1.

4, 3, 6, 9, 8, 11, 1, 2, 12, 15, 16, 13, 18, 7, 5, 21, 30, 23, 22, 17, 19, 25, 10, 27, 34, 29, 32, 31, 20, 24, 36, 37, 42, 39, 46, 47, 33, 26, 35, 41, 44, 43, 28, 53, 48, 51, 50, 49, 62, 55, 56, 61, 66, 38, 14, 59, 52, 45, 68, 63, 40, 67, 64, 57, 72, 71, 70, 73, 74, 77, 80, 79

Offset: 1

Author

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

Keywords

• nonn

Comments

By numerical explorations up to 50k terms, it seems to be an "infinite braid", i.e. it consists of a single infinite cycle, without any fixed points or closed cycles.

Links

• Ferenc Adorjan, Table of n,a(n) for n=1..10000

Crossrefs

Inverse of A128755, Cf. A128756, A128757.

Programs

PARI

{pperm(n)= /* Returns a vector with n terms of the sequence */
local(m,q,v,x,j,ap);j=n+prime(n+6)-prime(n);v=vector(j);x=vector(n);
for(i=1,j,v[i]=i);for(i=1,j,ap=prime(i+1)-prime(i)-1;q=v[i];v[i]=v[i-ap];v[i-ap]=q);
for(i=1,n,x[i]=v[i]);return(x)}