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 1-4 of 4 results.

A134267 a(n) = |A090964(n+1) - A090964(n)|.

Original entry on oeis.org

3, 2, 3, 2, 5, 2, 3, 2, 5, 2, 3, 2, 5, 2, 3, 2, 5, 2, 3, 2, 5, 2, 3, 2, 5, 2, 3, 2, 5, 2, 3, 2, 5, 2, 3, 2, 5, 2, 3, 2, 5
Offset: 1

Views

Author

Giovanni Teofilatto, Jan 15 2008

Keywords

Comments

Except for initial term, periodic sequence with period 2 3 2 5.

Links

Crossrefs

Cf. A090964.

Programs

  • Mathematica
    LinearRecurrence[{0,0,0,1},{3,2,3,2,5},50] (* or *) PadRight[{3},50,{5,2,3,2}] (* Harvey P. Dale, May 13 2023 *)

A116468 Permutation of natural numbers generated by 2-rowed array shown below.

Original entry on oeis.org

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

Views

Author

Giovanni Teofilatto, Mar 17 2006

Keywords

Comments

2 3 6 7 10 11 14 15 ... integers congruent to 2 or 3 mod 4
1 4 5 8 9 12 13 16 ... integers congruent to 0 or 1 mod 4

References

  • M. Cerasoli, F. Eugeni and M. Protasi, Elementi di Matematica Discreta, Bologna 1988
  • Emanuele Munarini and Norma Zagaglia Salvi, Matematica Discreta,UTET, CittaStudiEdizioni, Milano 1997

Links

Crossrefs

Cf. A090964.

Formula

For n>2, a(n+4k) = a(n) + 4k, with k>=1.
G.f.: x*(2+x-2*x^2+5*x^3-4*x^4+2*x^5)/(1-x-x^4+x^5). - Philippe Deléham, Dec 02 2016

Extensions

Terms corrected by R. J. Mathar, Oct 25 2011

A091578 Permutation of primes generated by 2-rowed array shown below.

Original entry on oeis.org

2, 7, 3, 11, 5, 19, 13, 23, 17, 37, 29, 41, 31, 53, 43, 59, 47, 71, 61, 73, 67, 89, 79, 97, 83, 107, 101, 109, 103, 131, 113, 137, 127, 151, 139, 157, 149, 173, 163, 179, 167, 193, 181, 197, 191, 223, 199, 227, 211, 239, 229, 241, 233, 263, 251, 257
Offset: 1

Views

Author

Giovanni Teofilatto, Mar 05 2004; corrected and extended Oct 13 2006, Oct 15 2006

Keywords

Comments

2 7 11 19 23 37 41 53 59 ... (A060191)
3 5 13 17 29 31 43 47 61 ... (A060192)

Crossrefs

Cf. A090964.

Formula

a(n) = A000040(A090964(n)). a(n) = A000040(a(k+8) = a(k)+8).

A115659 Permutation of natural numbers generated by 2-rowed array shown below.

Original entry on oeis.org

0, 3, 1, 4, 2, 7, 5, 8, 6, 11, 9, 12, 10, 15, 13, 16, 14, 19, 17, 20, 18, 23, 21, 24, 22, 27, 25, 28, 26, 31, 29, 32, 30, 35, 33, 36, 34, 39, 37, 40, 38, 43, 41, 44, 42, 47, 45, 48, 46, 51, 49, 52, 50, 55, 53, 56, 54, 59, 57, 60, 58, 63, 61, 64, 62
Offset: 1

Views

Author

Giovanni Teofilatto, Mar 18 2006

Keywords

Comments

0 3 4 7 8 11 12 15 ...: integers congruent to 0 or 3 mod 4.
1 2 5 6 9 10 13 14 ...: integers congruent to 1 or 2 mod 4.
Essentially the same as A067060. - Hugo Pfoertner, Jun 16 2024

References

  • M. Cerasoli, F. Eugeni and M. Protasi, Elementi di Matematica Discreta, Bologna 1988.
  • Emanuele Munarini and Norma Zagaglia Salvi, Matematica Discreta, UTET, CittaStudiEdizioni, Milano 1997.

Links

Crossrefs

Cf. A067060, A090964, A116468.

Programs

  • Magma
    I:=[0, 3, 1, 4, 2, 7]; [n le 6 select I[n] else Self(n-1)+Self(n-4)-Self(n-5): n in [1..70]]; // Vincenzo Librandi, Dec 02 2016
  • Mathematica
    Join[{0}, LinearRecurrence[{1, 0, 0, 1, -1}, {3, 1, 4, 2, 7}, 70]] (* Vincenzo Librandi, Dec 02 2016 *)

Formula

For n>0, a(n+4k) = a(n) + 4k, with k>=0.
G.f.: x^2*(3 - 2*x + 3*x^2 - 2*x^3 + 2*x^4)/(1 - x - x^4 + x^5). - Philippe Deléham, Dec 02 2016

Extensions

Entries corrected by R. J. Mathar, Oct 25 2011
Showing 1-4 of 4 results.

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