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 1-6 of 6 results.

A332113 a(n) = (10^(2n+1)-1)/9 + 2*10^n.

Original entry on oeis.org

3, 131, 11311, 1113111, 111131111, 11111311111, 1111113111111, 111111131111111, 11111111311111111, 1111111113111111111, 111111111131111111111, 11111111111311111111111, 1111111111113111111111111, 111111111111131111111111111, 11111111111111311111111111111, 1111111111111113111111111111111
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2020

Keywords

Comments

See A107123 = {0, 1, 2, 19, 97, 9818, ...} for the indices of primes.

Links

Crossrefs

Cf. (A077779-1)/2 = A107123: indices of primes; A331864 & A331865 (non-palindromic variants).
Cf. A002275 (repunits R_n = (10^n-1)/9), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
Cf. A332123 .. A332193 (variants with different repeated digit 2, ..., 9).
Cf. A332112 .. A332119 (variants with different middle digit 2, ..., 9).

Programs

  • Maple
    A332113 := n -> (10^(2*n+1)-1)/9+2*10^n;
  • Mathematica
    Array[(10^(2 # + 1)-1)/9 + 2*10^# &, 15, 0]
  • PARI
    apply( {A332113(n)=10^(n*2+1)\9+2*10^n}, [0..15])
  • Python
    def A332113(n): return 10**(n*2+1)//9+2*10**n

Formula

a(n) = A138148(n) + 3*10^n = A002275(2n+1) + 2*10^n.
G.f.: (3 - 202*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.

A332123 a(n) = 2*(10^(2n+1)-1)/9 + 10^n.

Original entry on oeis.org

3, 232, 22322, 2223222, 222232222, 22222322222, 2222223222222, 222222232222222, 22222222322222222, 2222222223222222222, 222222222232222222222, 22222222222322222222222, 2222222222223222222222222, 222222222222232222222222222, 22222222222222322222222222222, 2222222222222223222222222222222
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. A332113 .. A332193 (variants with different repeated digit 1, ..., 9).
Cf. A332120 .. A332129 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332123 := n -> 2*(10^(2*n+1)-1)/9+10^n;
  • Mathematica
    Array[2 (10^(2 # + 1)-1)/9 + 10^# &, 15, 0]
  • PARI
    apply( {A332123(n)=10^(n*2+1)\9*2+10^n}, [0..15])
  • Python
    def A332123(n): return 10**(n*2+1)//9*2+10**n

Formula

a(n) = 2*A138148(n) + 3*10^n = A002276(2n+1) + 10^n.
G.f.: (3 - 101*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.

A332143 a(n) = 4*(10^(2*n+1)-1)/9 - 10^n.

Original entry on oeis.org

3, 434, 44344, 4443444, 444434444, 44444344444, 4444443444444, 444444434444444, 44444444344444444, 4444444443444444444, 444444444434444444444, 44444444444344444444444, 4444444444443444444444444, 444444444444434444444444444, 44444444444444344444444444444, 4444444444444443444444444444444
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2020

Keywords

Links

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002278 (4*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. A332140 .. A332149 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332143 := n -> 4*(10^(2*n+1)-1)/9-10^n;
  • Mathematica
    Array[4 (10^(2 # + 1)-1)/9 - 10^# &, 15, 0]
  • PARI
    apply( {A332143(n)=10^(n*2+1)\9*4-10^n}, [0..15])
  • Python
    def A332143(n): return 10**(n*2+1)//9*4-10**n

Formula

a(n) = 4*A138148(n) + 3*10^n = A002278(2n+1) - 10^n.
G.f.: (3 + 101*x - 500*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.

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.

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.

A332163 a(n) = 6*(10^(2*n+1)-1)/9 - 3*10^n.

Original entry on oeis.org

3, 636, 66366, 6663666, 666636666, 66666366666, 6666663666666, 666666636666666, 66666666366666666, 6666666663666666666, 666666666636666666666, 66666666666366666666666, 6666666666663666666666666, 666666666666636666666666666, 66666666666666366666666666666, 6666666666666663666666666666666
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2020

Keywords

Links

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002280 (6*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. A332160 .. A332169 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332163 := n -> 6*(10^(2*n+1)-1)/9-3*10^n;
  • Mathematica
    Array[6 (10^(2 # + 1)-1)/9 - 3*10^# &, 15, 0]
  • PARI
    apply( {A332163(n)=10^(n*2+1)\9*6-3*10^n}, [0..15])
  • Python
    def A332163(n): return 10**(n*2+1)//9*6-3*10**n

Formula

a(n) = 6*A138148(n) + 3*10^n = A002280(2n+1) - 3*10^n = 3*A332121(n).
G.f.: (3 + 303*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.
Showing 1-6 of 6 results.

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

Content is available under The OEIS End-User License Agreement.