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 1-6 of 6 results.

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.

Original entry on oeis.org

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

Views

Author

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

Keywords

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

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)}

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)

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)

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 1-6 of 6 results.

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