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 1-10 of 15 results. Next

A332190 a(n) = 10^(2n+1) - 1 - 9*10^n.

Original entry on oeis.org

0, 909, 99099, 9990999, 999909999, 99999099999, 9999990999999, 999999909999999, 99999999099999999, 9999999990999999999, 999999999909999999999, 99999999999099999999999, 9999999999990999999999999, 999999999999909999999999999, 99999999999999099999999999999, 9999999999999990999999999999999
Offset: 0

Views

Author

M. F. Hasler, Feb 08 2020

Keywords

Links

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002283 (9*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits only), A002113 (palindromes).
Cf. A332120 .. A332180 (variants with different repeated digit 2, ..., 8).
Cf. A332191 .. A332197, A181965 (variants with different middle digit 1, ..., 8).

Programs

  • Maple
    A332190 := n -> 10^(2*n+1)-1-9*10^n;
  • Mathematica
    Array[10^(2 # + 1)-1-9*10^# &, 15, 0]
LinearRecurrence[{111,-1110,1000},{0,909,99099},20] (* Harvey P. Dale, May 28 2021 *)
  • PARI
    apply( {A332190(n)=10^(n*2+1)-1-9*10^n}, [0..15])
  • Python
    def A332190(n): return 10**(n*2+1)-1-9*10^n

Formula

a(n) = 9*A138148(n) = A002283(2n+1) - A011557(n).
G.f.: 9*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.

A332121 a(n) = 2*(10^(2n+1)-1)/9 - 10^n.

Original entry on oeis.org

1, 212, 22122, 2221222, 222212222, 22222122222, 2222221222222, 222222212222222, 22222222122222222, 2222222221222222222, 222222222212222222222, 22222222222122222222222, 2222222222221222222222222, 222222222222212222222222222, 22222222222222122222222222222, 2222222222222221222222222222222
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. A332120 .. A332129 (variants with different middle digit 0, ..., 9).
Cf. A332131 .. A332191 (variants with different repeated digit 3, ..., 9).

Programs

  • Maple
    A332121 := n -> 2*(10^(2*n+1)-1)/9-10^n;
  • Mathematica
    Array[2 (10^(2 # + 1)-1)/9 - 10^# &, 15, 0]
  • PARI
    apply( {A332121(n)=10^(n*2+1)\9*2-10^n}, [0..15])
  • Python
    def A332121(n): return 10**(n*2+1)//9*2-10**n

Formula

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

A332129 a(n) = 2*(10^(2n+1)-1)/9 + 7*10^n.

Original entry on oeis.org

9, 292, 22922, 2229222, 222292222, 22222922222, 2222229222222, 222222292222222, 22222222922222222, 2222222229222222222, 222222222292222222222, 22222222222922222222222, 2222222222229222222222222, 222222222222292222222222222, 22222222222222922222222222222, 2222222222222229222222222222222
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. A332119 .. A332189 (variants with different repeated digit 1, ..., 8).
Cf. A332120 .. A332128 (variants with different middle digit 0, ..., 8).

Programs

  • Maple
    A332129 := n -> 2*(10^(2*n+1)-1)/9+7*10^n;
  • Mathematica
    Array[2 (10^(2 # + 1)-1)/9 + 7*10^# &, 15, 0]
LinearRecurrence[{111,-1110,1000},{9,292,22922},20] (* Harvey P. Dale, Jun 25 2020 *)
  • PARI
    apply( {A332129(n)=10^(n*2+1)\9*2+7*10^n}, [0..15])
  • Python
    def A332129(n): return 10**(n*2+1)//9*2+7*10**n

Formula

a(n) = 2*A138148(n) + 9*10^n = A002276(2n+1) + 7*10^n.
G.f.: (9 - 707*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.

A332180 a(n) = 8*(10^(2n+1)-1)/9 - 8*10^n.

Original entry on oeis.org

0, 808, 88088, 8880888, 888808888, 88888088888, 8888880888888, 888888808888888, 88888888088888888, 8888888880888888888, 888888888808888888888, 88888888888088888888888, 8888888888880888888888888, 888888888888808888888888888, 88888888888888088888888888888, 8888888888888880888888888888888
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. A332120 .. A332190 (variants with different repeated digit 2, ..., 9).
Cf. A332181 .. A332189 (variants with different middle digit 1, ..., 9).
Subsequence of A006072 (numbers with mirror symmetry about middle), A153806 (strobogrammatic cyclops numbers), and A204095 (numbers whose decimal digits are in {0,8}).

Programs

  • Maple
    A332180 := n -> 8*((10^(2*n+1)-1)/9-10^n);
  • Mathematica
    Array[8 ((10^(2 # + 1)-1)/9 - 10^#) &, 15, 0]
  • PARI
    apply( {A332180(n)=(10^(n*2+1)\9-10^n)*8}, [0..15])
  • Python
    def A332180(n): return (10**(n*2+1)//9-10**n)*8

Formula

a(n) = 8*A138148(n) = A002282(2n+1) - 8*10^n.
G.f.: 8*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.
E.g.f.: 8*exp(x)*(10*exp(99*x) - 9*exp(9*x) - 1)/9. - Stefano Spezia, Jul 13 2024

A332130 a(n) = (10^(2n+1)-1)/3 - 3*10^n.

Original entry on oeis.org

0, 303, 33033, 3330333, 333303333, 33333033333, 3333330333333, 333333303333333, 33333333033333333, 3333333330333333333, 333333333303333333333, 33333333333033333333333, 3333333333330333333333333, 333333333333303333333333333, 33333333333333033333333333333, 3333333333333330333333333333333
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2020

Keywords

Links

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002277 (3*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
Cf. A332120 .. A332190 (variants with different repeated digit 2, ..., 9).
Cf. A332131 .. A332139 (variants with different middle digit 1, ..., 9).

Programs

  • Maple
    A332130 := n -> (10^(2*n+1)-1)/3-3*10^n;
  • Mathematica
    Array[ ((10^(2 # + 1)-1)/3 - 3*10^#) &, 15, 0]
  • PARI
    apply( {A332130(n)=10^(n*2+1)\3-3*10^n}, [0..15])
  • Python
    def A332130(n): return 10**(n*2+1)//3-3*10**n

Formula

a(n) = 3*A138148(n) = A002277(2n+1) - 3*10^n.
G.f.: 3*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.
E.g.f.: exp(x)*(10*exp(99*x) - 9*exp(9*x) - 1)/3. - Stefano Spezia, Jul 13 2024

A332140 a(n) = 4*(10^(2n+1)-1)/9 - 4*10^n.

Original entry on oeis.org

0, 404, 44044, 4440444, 444404444, 44444044444, 4444440444444, 444444404444444, 44444444044444444, 4444444440444444444, 444444444404444444444, 44444444444044444444444, 4444444444440444444444444, 444444444444404444444444444, 44444444444444044444444444444, 4444444444444440444444444444444
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. A332120 .. A332190 (variants with different repeated digit 2, ..., 9).
Cf. A332141 .. A332149 (variants with different middle digit 1, ..., 9).

Programs

  • Maple
    A332140 := n -> 4*((10^(2*n+1)-1)/9-10^n);
  • Mathematica
    Array[4 ((10^(2 # + 1)-1)/9 - 10^#) &, 15, 0]
LinearRecurrence[{111,-1110,1000},{0,404,44044},20] (* Harvey P. Dale, Jul 06 2021 *)
  • PARI
    apply( {A332140(n)=(10^(n*2+1)\9-10^n)*4}, [0..15])
  • Python
    def A332140(n): return (10**(n*2+1)//9-10**n)*4

Formula

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

A332150 a(n) = 5*(10^(2n+1)-1)/9 - 5*10^n.

Original entry on oeis.org

0, 505, 55055, 5550555, 555505555, 55555055555, 5555550555555, 555555505555555, 55555555055555555, 5555555550555555555, 555555555505555555555, 55555555555055555555555, 5555555555550555555555555, 555555555555505555555555555, 55555555555555055555555555555, 5555555555555550555555555555555
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. A332120 .. A332190 (variants with different repeated digit 2, ..., 9).
Cf. A332151 .. A332159 (variants with different middle digit 1, ..., 9).

Programs

  • Maple
    A332150 := n -> 5*((10^(2*n+1)-1)/9-10^n);
  • Mathematica
    Array[5 ((10^(2 # + 1)-1)/9 - 10^#) &, 15, 0]
Table[With[{c=PadRight[{},n,5]},FromDigits[Join[c,{0},c]]],{n,0,15}] (* or *) LinearRecurrence[{111,-1110,1000},{0,505,55055},20] (* Harvey P. Dale, Jun 30 2025 *)
  • PARI
    apply( {A332150(n)=(10^(n*2+1)\9-10^n)*5}, [0..15])
  • Python
    def A332150(n): return (10**(n*2+1)//9-10**n)*5

Formula

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

A332160 a(n) = 6*(10^(2n+1)-1)/9 - 6*10^n.

Original entry on oeis.org

0, 606, 66066, 6660666, 666606666, 66666066666, 6666660666666, 666666606666666, 66666666066666666, 6666666660666666666, 666666666606666666666, 66666666666066666666666, 6666666666660666666666666, 666666666666606666666666666, 66666666666666066666666666666, 6666666666666660666666666666666
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. A332161 .. A332169 (variants with different middle digit 1, ..., 9).
Cf. A332120 .. A332190 (variants with different repeated digit 2, ..., 9).

Programs

  • Maple
    A332160 := n -> 6*((10^(2*n+1)-1)/9-10^n);
  • Mathematica
    Array[6 ((10^(2 # + 1)-1)/9 - 10^#) &, 15, 0]
  • PARI
    apply( {A332160(n)=(10^(n*2+1)\9-10^n)*6}, [0..15])
  • Python
    def A332160(n): return (10**(n*2+1)//9-10**n)*6

Formula

a(n) = 6*A138148(n) = A002280(2n+1) - 6*10^n.
G.f.: 6*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.

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.

A332124 a(n) = 2*(10^(2n+1)-1)/9 + 2*10^n.

Original entry on oeis.org

4, 242, 22422, 2224222, 222242222, 22222422222, 2222224222222, 222222242222222, 22222222422222222, 2222222224222222222, 222222222242222222222, 22222222222422222222222, 2222222222224222222222222, 222222222222242222222222222, 22222222222222422222222222222, 2222222222222224222222222222222
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. A332114 .. A332194 (variants with different repeated digit 1, ..., 9).
Cf. A332120 .. A332129 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332124 := n -> 2*((10^(2*n+1)-1)/9+10^n);
  • Mathematica
    Array[2 ((10^(2 # + 1)-1)/9 + 10^#) &, 15, 0]
Table[FromDigits[Join[PadRight[{},n,2],{4},PadRight[{},n,2]]],{n,0,20}] (* or *) LinearRecurrence[{111,-1110,1000},{4,242,22422},20](* Harvey P. Dale, Mar 06 2023 *)
  • PARI
    apply( {A332124(n)=(10^(n*2+1)\9+10^n)*2}, [0..15])
  • Python
    def A332124(n): return (10**(n*2+1)//9+10**n)*2

Formula

a(n) = 2*A138148(n) + 4*10^n = A002276(2n+1) + 2*10^n = 2*A332112(n).
G.f.: (4 - 202*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.
Showing 1-10 of 15 results. Next

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