cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A129675 Inverse permutation to A129674.

Original entry on oeis.org

3, 2, 1, 5, 7, 4, 6, 9, 15, 8, 11, 10, 12, 14, 13, 17, 21, 16, 19, 18, 20, 23, 27, 22, 24, 26, 25, 29, 31, 28, 30, 33, 37, 32, 35, 34, 36, 39, 43, 38, 40, 42, 41, 45, 51, 44, 47, 46, 48, 50, 49, 53, 55, 52, 54, 57, 63, 56, 59, 58, 60, 62, 61, 65, 69, 64, 67, 66, 68, 71, 75, 70
Offset: 1

Views

Author

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

Keywords

Comments

The inversion maintains the cyclic characteristics as described in A129674.

Links

Crossrefs

Inverse of A129674, Cf. A128754, A128755, A129679 and A001969.

Programs

  • PARI
    {pinverse(v)= /* Permutation inverse of a positive sequence */
local(n,m,x);n=matsize(v)[2]; x=vector(n);
for(i=1,n,if(v[i]<=n,x[v[i]]=i)); return(x)}
a=pinverse(A129674)

A129678 Distance sequence of A129674: A129674(n)-n.

Original entry on oeis.org

2, 0, -2, 2, -1, 1, -2, 2, -1, 2, 0, 1, 2, 0, -6, 2, -1, 2, 0, 1, -4, 2, -1, 1, 2, 0, -4, 2, -1, 1, -2, 2, -1, 2, 0, 1, -4, 2, -1, 1, 2, 0, -4, 2, -1, 2, 0, 1, 2, 0, -6, 2, -1, 1, -2, 2, -1, 2, 0, 1, 2, 0, -6, 2, -1, 2, 0, 1, -4, 2, -1, 1, 2, 0, -4, 2, -1, 2, 0, 1, 2, 0, -6, 2, -1, 1, -2, 2, -1, 2, 0, 1, -4, 2, -1, 1, 2, 0, -4
Offset: 1

Views

Author

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

Keywords

Comments

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

Crossrefs

Distance of A129674, Cf. A129679, A129680, A129681 and 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

Views

Author

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

Keywords

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

Crossrefs

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

Programs

  • 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)
Showing 1-3 of 3 results.

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