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 1-8 of 8 results.

A128755 Inverse of A128754.

Original entry on oeis.org

7, 8, 2, 1, 15, 3, 14, 5, 4, 23, 6, 9, 12, 55, 10, 11, 20, 13, 21, 29, 16, 19, 18, 30, 22, 38, 24, 43, 26, 17, 28, 27, 37, 25, 39, 31, 32, 54, 34, 61, 40, 33, 42, 41, 58, 35, 36, 45, 48, 47, 46, 57, 44, 78, 50, 51, 64, 76, 56, 74, 52, 49, 60, 63, 77, 53, 62, 59, 83, 67, 66, 65
Offset: 1

Views

Author

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

Keywords

Comments

Seemingly the inversion maintains the characteristics of being an "infinite braid".

Links

Crossrefs

Inverse of A128754, Cf. A128756, A128757.

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)}
pinverse(A128754)

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.

Original entry on oeis.org

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

Views

Author

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

Keywords

Comments

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

Links

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

A128757 Inverse permutation to A128756.

Original entry on oeis.org

9, 5, 2, 11, 10, 1, 4, 23, 8, 20, 6, 7, 24, 3, 12, 27, 14, 64, 21, 13, 16, 17, 18, 41, 49, 15, 26, 33, 28, 32, 22, 25, 30, 29, 38, 19, 39, 53, 34, 59, 36, 35, 40, 37, 42, 72, 44, 31, 95, 45, 46, 43, 52, 56, 48, 51, 75, 47, 66, 85, 58, 55, 54, 57, 71, 61, 50, 63, 87, 65, 62, 78
Offset: 1

Views

Author

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

Keywords

Comments

Seemingly the inversion maintains the characteristics of being an "infinite braid".

Links

Crossrefs

Inverse of A128756, cf. A128754, A128755 and A000959.

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(A128756)

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

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 (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

Crossrefs

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

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(A001969)

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)

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)

A129677 Inverse permutation to A129676.

Original entry on oeis.org

2, 6, 1, 4, 3, 5, 8, 12, 7, 9, 11, 10, 14, 20, 13, 16, 15, 17, 19, 18, 22, 24, 21, 23, 26, 30, 25, 28, 27, 29, 32, 36, 31, 33, 35, 34, 38, 40, 37, 39, 42, 48, 41, 44, 43, 45, 47, 46, 50, 54, 49, 52, 51, 53, 56, 60, 55, 57, 59, 58, 62, 68, 61, 64, 63, 65, 67, 66, 70, 72, 69, 71
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 described in A129676.

Links

Crossrefs

Inverse of A129676, cf. A128754, A128755, A129681 and A000069.

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(A129676)

A130264 Inverse of A014321, which is permutation of positive integers assuming Polignac's conjecture is true.

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 5, 13, 8, 9, 10, 12, 14, 15, 16, 17, 11, 18, 24, 21, 20, 19, 31, 23, 26, 22, 28, 32, 30, 29, 27, 33, 36, 34, 37, 25, 44, 39, 38, 48, 40, 46, 35, 49, 45, 51, 53, 41, 50, 43, 57, 56, 52, 62, 58, 42, 47, 68, 54, 60, 63, 71, 59, 65, 67, 55, 72, 70, 64, 73, 75, 76
Offset: 1

Views

Author

Ferenc Adorjan (fadorjan(AT)freemail.hu or ferencadorjan(AT)gmail.com), May 20 2007

Keywords

Links

Crossrefs

Inverse of A014321, Cf. A128754, A128755.
Showing 1-8 of 8 results.

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