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.

Previous Showing 11-14 of 14 results.

A332183 a(n) = 8*(10^(2n+1)-1)/9 - 5*10^n.

Original entry on oeis.org

3, 838, 88388, 8883888, 888838888, 88888388888, 8888883888888, 888888838888888, 88888888388888888, 8888888883888888888, 888888888838888888888, 88888888888388888888888, 8888888888883888888888888, 888888888888838888888888888, 88888888888888388888888888888, 8888888888888883888888888888888
Offset: 0

Views

Author

M. F. Hasler, Feb 08 2020

Keywords

Links

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002282 (8*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits only).
Cf. A332113 .. A332193 (variants with different repeated digit 1, ..., 9).
Cf. A332180 .. A332189 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332183 := n -> 8*(10^(2*n+1)-1)/9-5*10^n;
  • Mathematica
    Array[8 (10^(2 # + 1)-1)/9 - 5*10^# &, 15, 0]
  • PARI
    apply( {A332183(n)=10^(n*2+1)\9*8-5*10^n}, [0..15])
  • Python
    def A332183(n): return 10**(n*2+1)//9*8-5*10**n

Formula

a(n) = 8*A138148(n) + 3*10^n = A002282(2n+1) - 5*10^n.
G.f.: (3 + 505*x - 1300*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).
a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.

A332184 a(n) = 8*(10^(2n+1)-1)/9 - 4*10^n.

Original entry on oeis.org

4, 848, 88488, 8884888, 888848888, 88888488888, 8888884888888, 888888848888888, 88888888488888888, 8888888884888888888, 888888888848888888888, 88888888888488888888888, 8888888888884888888888888, 888888888888848888888888888, 88888888888888488888888888888, 8888888888888884888888888888888
Offset: 0

Views

Author

M. F. Hasler, Feb 08 2020

Keywords

Links

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002282 (8*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits only).
Cf. A332180 .. A332189 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332184 := n -> 8*(10^(2*n+1)-1)/9-4*10^n;
  • Mathematica
    Array[8 (10^(2 # + 1)-1)/9- 4*10^# &, 15, 0]
  • PARI
    apply( {A332184(n)=10^(n*2+1)\9*8-4*10^n}, [0..15])
  • Python
    def A332184(n): return 10**(n*2+1)//9*8-4*10**n

Formula

a(n) = 8*A138148(n) + 4*10^n = A002282(2n+1)- 4*10^n = 4*A332121(n).
G.f.: (4 + 404*x - 1200*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).
a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.

A332185 a(n) = 8*(10^(2n+1)-1)/9 - 3*10^n.

Original entry on oeis.org

5, 858, 88588, 8885888, 888858888, 88888588888, 8888885888888, 888888858888888, 88888888588888888, 8888888885888888888, 888888888858888888888, 88888888888588888888888, 8888888888885888888888888, 888888888888858888888888888, 88888888888888588888888888888, 8888888888888885888888888888888
Offset: 0

Views

Author

M. F. Hasler, Feb 08 2020

Keywords

Links

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002282 (8*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits only), A002113 (palindromes).
Cf. A332180 .. A332189 (variants with different middle digit 0, ..., 9).
Cf. A332115 .. A332195 (variants with different "wing" digit 1, ..., 9).

Programs

  • Maple
    A332185 := n -> 8*(10^(2*n+1)-1)/9-3*10^n;
  • Mathematica
    Array[8 (10^(2 # + 1)-1)/9 - 3*10^# &, 15, 0]
  • PARI
    apply( {A332185(n)=10^(n*2+1)\9*8-3*10^n}, [0..15])
  • Python
    def A332185(n): return 10**(n*2+1)//9*8-3*10**n

Formula

a(n) = 8*A138148(n) + 5*10^n = A002282(2n+1) - 3*10^n.
G.f.: (5 + 303*x - 1100*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).
a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.

A332186 a(n) = 8*(10^(2n+1)-1)/9 - 2*10^n.

Original entry on oeis.org

6, 868, 88688, 8886888, 888868888, 88888688888, 8888886888888, 888888868888888, 88888888688888888, 8888888886888888888, 888888888868888888888, 88888888888688888888888, 8888888888886888888888888, 888888888888868888888888888, 88888888888888688888888888888, 8888888888888886888888888888888
Offset: 0

Views

Author

M. F. Hasler, Feb 08 2020

Keywords

Links

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002282 (8*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
Cf. A332180 .. A332189 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332186 := n -> 8*(10^(2*n+1)-1)/9-2*10^n;
  • Mathematica
    Array[8 (10^(2 # + 1)-1)/9 - 2*10^# &, 15, 0]
LinearRecurrence[{111,-1110,1000},{6,868,88688},20] (*or *) Table[FromDigits[Join[PadRight[ {},n,8],PadRight[ {6},n+1,8]]],{n,0,20}] (* Harvey P. Dale, May 30 2023 *)
  • PARI
    apply( {A332186(n)=10^(n*2+1)\9*8-2*10^n}, [0..15])
  • Python
    def A332186(n): return 10**(n*2+1)//9*8-2*10**n

Formula

a(n) = 8*A138148(n) + 6*10^n = A002282(2n+1) - 2*10^n = 2*A332143(n).
G.f.: (6 + 202*x - 1000*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).
a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.
E.g.f.: 2*exp(x)*(40*exp(99*x) - 9*exp(9*x) - 4)/9. - Stefano Spezia, Jul 13 2024
Previous Showing 11-14 of 14 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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