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 11-15 of 15 results.

A332125 a(n) = 2*(10^(2n+1)-1)/9 + 3*10^n.

Original entry on oeis.org

5, 252, 22522, 2225222, 222252222, 22222522222, 2222225222222, 222222252222222, 22222222522222222, 2222222225222222222, 222222222252222222222, 22222222222522222222222, 2222222222225222222222222, 222222222222252222222222222, 22222222222222522222222222222, 2222222222222225222222222222222
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2020

Keywords

Links

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002276 (2*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
Cf. A332115 .. A332195 (variants with different repeated digit 1, ..., 9).
Cf. A332120 .. A332129 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332125 := n -> 2*(10^(2*n+1)-1)/9+3*10^n;
  • Mathematica
    Array[2 (10^(2 # + 1)-1)/9 + 3*10^# &, 15, 0]
  • PARI
    apply( {A332125(n)=10^(n*2+1)\9*2+3*10^n}, [0..15])
  • Python
    def A332125(n): return 10**(n*2+1)//9*2+3*10**n

Formula

a(n) = 2*A138148(n) + 5*10^n = A002276(2n+1) + 3*10^n.
G.f.: (5 - 303*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.

A332126 a(n) = 2*(10^(2n+1)-1)/9 + 4*10^n.

Original entry on oeis.org

6, 262, 22622, 2226222, 222262222, 22222622222, 2222226222222, 222222262222222, 22222222622222222, 2222222226222222222, 222222222262222222222, 22222222222622222222222, 2222222222226222222222222, 222222222222262222222222222, 22222222222222622222222222222, 2222222222222226222222222222222
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2020

Keywords

Links

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002276 (2*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. A332120 .. A332129 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332126 := n -> 2*(10^(2*n+1)-1)/9+4*10^n;
  • Mathematica
    Array[2 (10^(2 # + 1)-1)/9 + 4*10^# &, 15, 0]
Table[FromDigits[Join[PadRight[{},n,2],{6},PadRight[{},n,2]]],{n,0,20}] (* or *) LinearRecurrence[{111,-1110,1000},{6,262,22622},20] (* Harvey P. Dale, Oct 17 2021 *)
  • PARI
    apply( {A332126(n)=10^(n*2+1)\9*2+4*10^n}, [0..15])
  • Python
    def A332126(n): return 10**(n*2+1)//9*2+4*10**n

Formula

a(n) = 2*A138148(n) + 6*10^n = A002276(2n+1) + 4*10^n = 2*A332113(n).
G.f.: (6 - 404*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.
E.g.f.: 2*exp(x)*(10*exp(99*x) + 18*exp(9*x) - 1)/9. - Stefano Spezia, Jul 13 2024

A332127 a(n) = 2*(10^(2n+1)-1)/9 + 5*10^n.

Original entry on oeis.org

7, 272, 22722, 2227222, 222272222, 22222722222, 2222227222222, 222222272222222, 22222222722222222, 2222222227222222222, 222222222272222222222, 22222222222722222222222, 2222222222227222222222222, 222222222222272222222222222, 22222222222222722222222222222, 2222222222222227222222222222222
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2020

Keywords

Links

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002276 (2*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. A332120 .. A332129 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332127 := n -> 2*(10^(2*n+1)-1)/9+5*10^n;
  • Mathematica
    Array[2 (10^(2 # + 1)-1)/9 + 5*10^# &, 15, 0]
  • PARI
    apply( {A332127(n)=10^(n*2+1)\9*2+5*10^n}, [0..15])
  • Python
    def A332127(n): return 10**(n*2+1)//9*2+5*10**n

Formula

a(n) = 2*A138148(n) + 7*10^n = A002276(2n+1) + 5*10^n.
G.f.: (7 - 505*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.

A332128 a(n) = 2*(10^(2n+1)-1)/9 + 6*10^n.

Original entry on oeis.org

8, 282, 22822, 2228222, 222282222, 22222822222, 2222228222222, 222222282222222, 22222222822222222, 2222222228222222222, 222222222282222222222, 22222222222822222222222, 2222222222228222222222222, 222222222222282222222222222, 22222222222222822222222222222, 2222222222222228222222222222222
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2020

Keywords

Links

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002276 (2*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. A332120 .. A332129 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332128 := n -> 2*(10^(2*n+1)-1)/9+6*10^n;
  • Mathematica
    Array[2 (10^(2 # + 1)-1)/9 + 6*10^# &, 15, 0]
  • PARI
    apply( {A332128(n)=10^(n*2+1)\9*2+6*10^n}, [0..15])
  • Python
    def A332128(n): return 10**(n*2+1)//9*2+6*10**n

Formula

a(n) = 2*A138148(n) + 8*10^n = A002276(2n+1) + 6*10^n = 2*A332114(n).
G.f.: (8 - 606*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.

A332170 a(n) = 7*(10^(2n+1)-1)/9 - 7*10^n.

Original entry on oeis.org

0, 707, 77077, 7770777, 777707777, 77777077777, 7777770777777, 777777707777777, 77777777077777777, 7777777770777777777, 777777777707777777777, 77777777777077777777777, 7777777777770777777777777, 777777777777707777777777777, 77777777777777077777777777777, 7777777777777770777777777777777
Offset: 0

Views

Author

M. F. Hasler, Feb 08 2020

Keywords

Links

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002281 (7*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits only), A002113 (palindromes).
Cf. A332120 .. A332190 (variants with different repeated digit 2, ..., 9).
Cf. A332171 .. A332179 (variants with different middle digit 1, ..., 9).

Programs

  • Maple
    A332170 := n -> 7*(10^(2*n+1)-1)/9-7*10^n;
  • Mathematica
    Array[7 ((10^(2 # + 1)-1)/9 - 10^#) &, 15, 0]
  • PARI
    apply( {A332170(n)=(10^(n*2+1)\9-10^n)*7}, [0..15])
  • Python
    def A332170(n): return (10**(n*2+1)//9-10^n)*7

Formula

a(n) = 7*A138148(n) = A002281(2n+1) - 7*A011557(n).
G.f.: 7*x*(101 - 200*x)/((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.
Previous Showing 11-15 of 15 results.

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