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.

A332159 a(n) = 5*(10^(2*n+1)-1)/9 + 4*10^n.

Original entry on oeis.org

9, 595, 55955, 5559555, 555595555, 55555955555, 5555559555555, 555555595555555, 55555555955555555, 5555555559555555555, 555555555595555555555, 55555555555955555555555, 5555555555559555555555555, 555555555555595555555555555, 55555555555555955555555555555, 5555555555555559555555555555555
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2020

Keywords

Links

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002279 (5*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
Cf. A332119 .. A332189 (variants with different repeated digit 1, ..., 8).
Cf. A332150 .. A332159 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332159 := n -> 5*(10^(2*n+1)-1)/9+4*10^n;
  • Mathematica
    Array[5 (10^(2 # + 1)-1)/9 + 4*10^# &, 15, 0]
Table[FromDigits[Join[PadRight[{},n,5],PadRight[{9},n+1,5]]],{n,0,20}] (* or *) LinearRecurrence[ {111,-1110,1000},{9,595,55955},20] (* Harvey P. Dale, May 31 2023 *)
  • PARI
    apply( {A332159(n)=10^(n*2+1)\9*5+4*10^n}, [0..15])
  • Python
    def A332159(n): return 10**(n*2+1)//9*5+4*10**n

Formula

a(n) = 5*A138148(n) + 9*10^n = A002279(2n+1) + 4*10^n.
G.f.: (9 - 404*x - 100*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.

A332151 a(n) = 5*(10^(2*n+1)-1)/9 - 4*10^n.

Original entry on oeis.org

1, 515, 55155, 5551555, 555515555, 55555155555, 5555551555555, 555555515555555, 55555555155555555, 5555555551555555555, 555555555515555555555, 55555555555155555555555, 5555555555551555555555555, 555555555555515555555555555, 55555555555555155555555555555, 5555555555555551555555555555555
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2020

Keywords

Links

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002279 (5*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
Cf. A332121 .. A332191 (variants with different repeated digit 2, ..., 9).
Cf. A332150 .. A332159 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332151 := n -> 5*(10^(2*n+1)-1)/9-4*10^n;
  • Mathematica
    Array[5 (10^(2 # + 1)-1)/9 - 4*10^# &, 15, 0]
Table[With[{c=PadRight[{},n,5]},FromDigits[Join[c,{1},c]]],{n,0,20}] (* Harvey P. Dale, Mar 16 2021 *)
  • PARI
    apply( {A332151(n)=10^(n*2+1)\9*5-4*10^n}, [0..15])
  • Python
    def A332151(n): return 10**(n*2+1)//9*5-4*10**n

Formula

a(n) = 5*A138148(n) + 10^n = A002279(2n+1) - 4*10^n.
G.f.: (1 + 404*x - 900*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.

A332152 a(n) = 5*(10^(2*n+1)-1)/9 - 3*10^n.

Original entry on oeis.org

2, 525, 55255, 5552555, 555525555, 55555255555, 5555552555555, 555555525555555, 55555555255555555, 5555555552555555555, 555555555525555555555, 55555555555255555555555, 5555555555552555555555555, 555555555555525555555555555, 55555555555555255555555555555, 5555555555555552555555555555555
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2020

Keywords

Links

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002279 (5*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
Cf. A332112 .. A332192 (variants with different repeated digit 1, ..., 9).
Cf. A332150 .. A332159 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332152 := n -> 5*(10^(2*n+1)-1)/9-3*10^n;
  • Mathematica
    Array[5 (10^(2 # + 1)-1)/9 - 3*10^# &, 15, 0]
  • PARI
    apply( {A332152(n)=10^(n*2+1)\9*5-3*10^n}, [0..15])
  • Python
    def A332152(n): return 10**(n*2+1)//9*5-3*10**n

Formula

a(n) = 5*A138148(n) + 2*10^n = A002279(2n+1) - 3*10^n.
G.f.: (2 + 303*x - 800*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.

A332153 a(n) = 5*(10^(2*n+1)-1)/9 - 2*10^n.

Original entry on oeis.org

3, 535, 55355, 5553555, 555535555, 55555355555, 5555553555555, 555555535555555, 55555555355555555, 5555555553555555555, 555555555535555555555, 55555555555355555555555, 5555555555553555555555555, 555555555555535555555555555, 55555555555555355555555555555, 5555555555555553555555555555555
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2020

Keywords

Links

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002279 (5*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
Cf. A332113 .. A332193 (variants with different repeated digit 1, ..., 9).
Cf. A332150 .. A332159 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332153 := n -> 5*(10^(2*n+1)-1)/9-2*10^n;
  • Mathematica
    Array[5 (10^(2 # + 1)-1)/9 - 2*10^# &, 15, 0]
  • PARI
    apply( {A332153(n)=10^(n*2+1)\9*5-2*10^n}, [0..15])
  • Python
    def A332153(n): return 10**(n*2+1)//9*5-2*10**n

Formula

a(n) = 5*A138148(n) + 3*10^n = A002279(2n+1) - 2*10^n.
G.f.: (3 + 202*x - 700*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.

A332154 a(n) = 5*(10^(2*n+1)-1)/9 - 10^n.

Original entry on oeis.org

4, 545, 55455, 5554555, 555545555, 55555455555, 5555554555555, 555555545555555, 55555555455555555, 5555555554555555555, 555555555545555555555, 55555555555455555555555, 5555555555554555555555555, 555555555555545555555555555, 55555555555555455555555555555, 5555555555555554555555555555555
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2020

Keywords

Links

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002279 (5*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
Cf. A332114 .. A332194 (variants with different repeated digit 1, ..., 9).
Cf. A332150 .. A332159 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332154 := n -> 5*(10^(2*n+1)-1)/9-10^n;
  • Mathematica
    Array[5 (10^(2 # + 1)-1)/9 - 10^# &, 15, 0]
LinearRecurrence[{111,-1110,1000},{4,545,55455},20] (* or *) Table[FromDigits[Join[PadRight[{},n,5],{4},PadRight[{},n,5]]],{n,0,20}] (* Harvey P. Dale, Mar 09 2025 *)
  • PARI
    apply( {A332154(n)=10^(n*2+1)\9*5-10^n}, [0..15])
  • Python
    def A332154(n): return 10**(n*2+1)//9*5-10**n

Formula

a(n) = 5*A138148(n) + 4*10^n = A002279(2n+1) - 10^n.
G.f.: (4 + 101*x - 600*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.

A332156 a(n) = 5*(10^(2*n+1)-1)/9 + 10^n.

Original entry on oeis.org

6, 565, 55655, 5556555, 555565555, 55555655555, 5555556555555, 555555565555555, 55555555655555555, 5555555556555555555, 555555555565555555555, 55555555555655555555555, 5555555555556555555555555, 555555555555565555555555555, 55555555555555655555555555555, 5555555555555556555555555555555
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2020

Keywords

Links

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002279 (5*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
Cf. A332116 .. A332196 (variants with different repeated digit 1, ..., 9).
Cf. A332150 .. A332159 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332156 := n -> 5*(10^(2*n+1)-1)/9+10^n;
  • Mathematica
    Array[5 (10^(2 # + 1)-1)/9 + 10^# &, 15, 0]
  • PARI
    apply( {A332156(n)=10^(n*2+1)\9*5+10^n}, [0..15])
  • Python
    def A332156(n): return 10**(n*2+1)//9*5+10**n

Formula

a(n) = 5*A138148(n) + 6*10^n = A002279(2n+1) + 10^n.
G.f.: (6 - 101*x - 400*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.: exp(x)*(50*exp(99*x) + 9*exp(9*x) - 5)/9. - Stefano Spezia, Jul 13 2024

A332157 a(n) = 5*(10^(2*n+1)-1)/9 + 2*10^n.

Original entry on oeis.org

7, 575, 55755, 5557555, 555575555, 55555755555, 5555557555555, 555555575555555, 55555555755555555, 5555555557555555555, 555555555575555555555, 55555555555755555555555, 5555555555557555555555555, 555555555555575555555555555, 55555555555555755555555555555, 5555555555555557555555555555555
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2020

Keywords

Links

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002279 (5*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
Cf. A332117 .. A332197 (variants with different repeated digit 1, ..., 9).
Cf. A332150 .. A332159 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332157 := n -> 5*(10^(2*n+1)-1)/9+2*10^n;
  • Mathematica
    Array[5 (10^(2 # + 1)-1)/9 + 2*10^# &, 15, 0]
  • PARI
    apply( {A332157(n)=10^(n*2+1)\9*5+2*10^n}, [0..15])
  • Python
    def A332157(n): return 10**(n*2+1)//9*5+2*10**n

Formula

a(n) = 5*A138148(n) + 7*10^n = A002279(2n+1) + 2*10^n.
G.f.: (7 - 202*x - 300*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.

A332158 a(n) = 5*(10^(2*n+1)-1)/9 + 3*10^n.

Original entry on oeis.org

8, 585, 55855, 5558555, 555585555, 55555855555, 5555558555555, 555555585555555, 55555555855555555, 5555555558555555555, 555555555585555555555, 55555555555855555555555, 5555555555558555555555555, 555555555555585555555555555, 55555555555555855555555555555, 5555555555555558555555555555555
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2020

Keywords

Links

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002279 (5*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
Cf. A332118 .. A332178, A181965 (variants with different repeated digit 1, ..., 9).
Cf. A332150 .. A332159 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332158 := n -> 5*(10^(2*n+1)-1)/9+3*10^n;
  • Mathematica
    Array[5 (10^(2 # + 1)-1)/9 + 3*10^# &, 15, 0]
  • PARI
    apply( {A332158(n)=10^(n*2+1)\9*5+3*10^n}, [0..15])
  • Python
    def A332158(n): return 10**(n*2+1)//9*5+3*10**n

Formula

a(n) = 5*A138148(n) + 8*10^n = A002279(2n+1) + 3*10^n.
G.f.: (8 - 303*x - 200*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.
Showing 1-8 of 8 results.

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