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.

A172430 Period length 10: repeat 2,1,6,7,0,3,4,9,8,5 .

Original entry on oeis.org

2, 1, 6, 7, 0, 3, 4, 9, 8, 5, 2, 1, 6, 7, 0, 3, 4, 9, 8, 5, 2, 1, 6, 7, 0, 3, 4, 9, 8, 5, 2, 1, 6, 7, 0, 3, 4, 9, 8, 5, 2, 1, 6, 7, 0, 3, 4, 9, 8, 5, 2, 1, 6, 7, 0, 3, 4, 9, 8, 5, 2, 1, 6, 7, 0, 3, 4, 9, 8, 5, 2, 1, 6, 7, 0, 3, 4, 9, 8, 5, 2, 1, 6, 7, 0, 3, 4, 9, 8, 5, 2, 1, 6, 7, 0, 3, 4, 9, 8, 5, 2, 1, 6, 7, 0, 3
Offset: 0

Views

Author

Paul Curtz, Feb 02 2010

Keywords

Comments

Also the decimal expansion of the rational number 240781665 / 1111111111 .

Formula

a(n) = A172285(n+1) mod 10.
G.f.: (2+x+6*x^2+7*x^3+3*x^5+4*x^6+9*x^7+8*x^8+5*x^9)/ ((1-x) * (1+x) * (x^4+x^3+x^2 +x+1)* (x^4-x^3+x^2-x+1)).
a(3*n) = A172423(n+2).

Extensions

Edited by R. J. Mathar, Feb 11 2010

A304580 Period 16: repeat 1,8,3,6,5,4,7,2,9,0,7,2,5,4,3,6.

Original entry on oeis.org

1, 8, 3, 6, 5, 4, 7, 2, 9, 0, 7, 2, 5, 4, 3, 6, 1, 8, 3, 6, 5, 4, 7, 2, 9, 0, 7, 2, 5, 4, 3, 6, 1, 8, 3, 6, 5, 4, 7, 2, 9, 0, 7, 2, 5, 4, 3, 6, 1, 8, 3, 6, 5, 4, 7, 2, 9, 0, 7, 2, 5, 4, 3, 6, 1, 8, 3, 6, 5, 4, 7, 2, 9, 0, 7, 2, 5, 4, 3, 6, 1, 8, 3, 6, 5, 4
Offset: 1

Views

Author

Halfdan Skjerning, May 15 2018

Keywords

Comments

Repeating sequences of alternating odd and even single digits that in pairs sum to 9, 11 or 7. Note that 1836547290725436 = 20202020197979796 / 11.

Links

Crossrefs

Cf. A172423, A172430, A304583.

Programs

  • Mathematica
    LinearRecurrence[{0,1,0,0,0,0,0,-1,0,1},{1,8,3,6,5,4,7,2,9,0},100] (* or *) PadRight[{},100,{1,8,3,6,5,4,7,2,9,0,7,2,5,4,3,6}] (* Harvey P. Dale, Sep 28 2021 *)
  • PARI
    Vec(x*(1 + 8*x + 2*x^2 - 2*x^3 + 2*x^4 - 2*x^5 + 2*x^6 - 2*x^7 + 3*x^8 + 6*x^9) / ((1 - x)*(1 + x)*(1 + x^8)) + O(x^50)) \\ Colin Barker, May 28 2018

Formula

From Colin Barker, May 28 2018: (Start)
G.f.: x*(1 + 8*x + 2*x^2 - 2*x^3 + 2*x^4 - 2*x^5 + 2*x^6 - 2*x^7 + 3*x^8 + 6*x^9) / ((1 - x)*(1 + x)*(1 + x^8)).
a(n) = a(n-2) - a(n-8) + a(n-10) for n > 10.
(End)

A304583 Period 18: repeat 1,8,3,6,5,4,7,2,9,0,9,2,7,4,5,6,3,8.

Original entry on oeis.org

1, 8, 3, 6, 5, 4, 7, 2, 9, 0, 9, 2, 7, 4, 5, 6, 3, 8, 1, 8, 3, 6, 5, 4, 7, 2, 9, 0, 9, 2, 7, 4, 5, 6, 3, 8, 1, 8, 3, 6, 5, 4, 7, 2, 9, 0, 9, 2, 7, 4, 5, 6, 3, 8, 1, 8, 3, 6, 5, 4, 7, 2, 9, 0, 9, 2, 7, 4, 5, 6, 3, 8, 1, 8, 3, 6, 5, 4, 7, 2, 9, 0, 9, 2, 7, 4
Offset: 1

Views

Author

Halfdan Skjerning, May 15 2018

Keywords

Comments

Repeating sequences of alternating odd and even single digits that in pairs sum to 9 or 11. Note that 183654729092745638 = 2020202020020202018 / 11.

Links

Crossrefs

Cf. A172423, A172430, A304580.

Programs

  • Mathematica
    PadRight[{},120,{1,8,3,6,5,4,7,2,9,0,9,2,7,4,5,6,3,8}] (* Harvey P. Dale, Feb 10 2024 *)
  • PARI
    Vec(x*(1 + 9*x + 11*x^2 + 9*x^3 + 11*x^4 + 9*x^5 + 11*x^6 + 9*x^7 + 11*x^8 + 8*x^9) / ((1 - x)*(1 + x)*(1 + x + x^2)*(1 + x^3 + x^6)) + O(x^50)) \\ Colin Barker, May 28 2018

Formula

From Colin Barker, May 28 2018: (Start)
G.f.: x*(1 + 9*x + 11*x^2 + 9*x^3 + 11*x^4 + 9*x^5 + 11*x^6 + 9*x^7 + 11*x^8 + 8*x^9) / ((1 - x)*(1 + x)*(1 + x + x^2)*(1 + x^3 + x^6)).
a(n) = -a(n-1) + a(n-9) + a(n-10) for n > 10.
(End)
Showing 1-3 of 3 results.

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