A129675 -id:A129675 - cp's OEIS frontend

A129679 Distance sequence of A129675: A129675(n)-n.

2, 0, -2, 1, 2, -2, -1, 1, 6, -2, 0, -2, -1, 0, -2, 1, 4, -2, 0, -2, -1, 1, 4, -2, -1, 0, -2, 1, 2, -2, -1, 1, 4, -2, 0, -2, -1, 1, 4, -2, -1, 0, -2, 1, 6, -2, 0, -2, -1, 0, -2, 1, 2, -2, -1, 1, 6, -2, 0, -2, -1, 0, -2, 1, 4, -2, 0, -2, -1, 1, 4, -2, -1, 0, -2, 1, 6, -2, 0, -2, -1, 0, -2, 1, 2, -2, -1, 1, 4, -2, 0, -2, -1, 1, 4, -2, -1, 0

Offset: 1

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

sign

The numbers in this sequence seem to be in the range of [ -2,6], but they are never 3 nor 5 (tested up to 10^4). The relative density of the values {-2,-1,0,1,2,4,6} asymptotically is {8,4,4,4,1,2,1}.

Distance of A129675, Cf. A129678, A129680, A129681 and A001969.

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).

Original entry on oeis.org

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

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

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.

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

{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)

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).

Original entry on oeis.org

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

Offset: 1

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

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.

Inverse of A129677, Cf. A128754, A128756, A129674, A129675, A129680 and A000069.

{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)

cp's OEIS Frontend

A129679 Distance sequence of A129675: A129675(n)-n.

Views

Author

Keywords

Comments

Crossrefs

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).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

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).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI