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 1-7 of 7 results.

A332179 a(n) = 7*(10^(2n+1)-1)/9 + 2*10^n.

Original entry on oeis.org

9, 797, 77977, 7779777, 777797777, 77777977777, 7777779777777, 777777797777777, 77777777977777777, 7777777779777777777, 777777777797777777777, 77777777777977777777777, 7777777777779777777777777, 777777777777797777777777777, 77777777777777977777777777777, 7777777777777779777777777777777
Offset: 0

Views

Author

M. F. Hasler, Feb 08 2020

Keywords

Comments

See A183183 = {1, 2, 8, 19, 20, 212, 280, ...} for the indices of primes.

Links

Crossrefs

Cf. A138148 (cyclops numbers with binary digits only).
Cf. (A077796-1)/2 = A183183: indices of primes.
Cf. A002275 (repunits R_n = [10^n/9]), A002281 (7*R_n), A011557 (10^n).
Cf. A332171 .. A332178 (variants with different middle digit 1, ..., 8).

Programs

  • Maple
    A332179 := n -> 7*(10^(n*2+1)-1)/9 + 2*10^n;
  • Mathematica
    Array[7 (10^(2 # + 1) - 1)/9 + 2*10^# &, 15, 0]
  • PARI
    apply( {A332179(n)=10^(n*2+1)\9*7+2*10^n}, [0..15])
  • Python
    def A332179(n): return 10**(n*2+1)//9*7+2*10^n

Formula

a(n) = 7*A138148(n) + 9*10^n.
G.f.: (9 - 202*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.

A332118 a(n) = (10^(2n+1) - 1)/9 + 7*10^n.

Original entry on oeis.org

8, 181, 11811, 1118111, 111181111, 11111811111, 1111118111111, 111111181111111, 11111111811111111, 1111111118111111111, 111111111181111111111, 11111111111811111111111, 1111111111118111111111111, 111111111111181111111111111, 11111111111111811111111111111, 1111111111111118111111111111111
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2020

Keywords

Comments

See A107648 = {1, 4, 6, 7, 384, 666, ...} for the indices of primes.

Links

Crossrefs

Cf. (A077791-1)/2 = A107648: indices of primes.
Cf. A002275 (repunits R_n = (10^n-1)/9), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes), A077798 (palindromic wing primes), A088281 (primes 1..1x1..1), A068160 (smallest of given length), A053701 (vertically symmetric numbers).
Cf. A332128 .. A332178, A181965 (variants with different repeated digit 2, ..., 9).
Cf. A332112 .. A332119 (variants with different middle digit 2, ..., 9).

Programs

  • Maple
    A332118 := n -> (10^(2*n+1)-1)/9+7*10^n;
  • Mathematica
    Array[(10^(2 # + 1)-1)/9 + 7*10^# &, 15, 0]
  • PARI
    apply( {A332118(n)=10^(n*2+1)\9+7*10^n}, [0..15])
  • Python
    def A332118(n): return 10**(n*2+1)//9+7*10**n

Formula

a(n) = A138148(n) + 8*10^n = A002275(2n+1) + 7*10^n.
G.f.: (8 - 707*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.

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.

A332138 a(n) = (10^(2*n+1)-1)/3 + 5*10^n.

Original entry on oeis.org

8, 383, 33833, 3338333, 333383333, 33333833333, 3333338333333, 333333383333333, 33333333833333333, 3333333338333333333, 333333333383333333333, 33333333333833333333333, 3333333333338333333333333, 333333333333383333333333333, 33333333333333833333333333333, 3333333333333338333333333333333
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2020

Keywords

Comments

See A183177 = {1, 7, 85, 94, 273, 356, ...} for the indices of primes.

Links

Crossrefs

Cf. (A077792-1)/2 = A183177: indices of primes.
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. A332118 .. A332178, A181965 (variants with different repeated digit 1, ..., 9).
Cf. A332130 .. A332139 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332138 := n -> (10^(2*n+1)-1)/3+5*10^n;
  • Mathematica
    Array[ (10^(2 # + 1)-1)/3 + 5*10^# &, 15, 0]
  • PARI
    apply( {A332138(n)=10^(n*2+1)\3+5*10^n}, [0..15])
  • Python
    def A332138(n): return 10**(n*2+1)//3+5*10**n

Formula

a(n) = 3*A138148(n) + 8*10^n = A002277(2n+1) + 5*10^n.
G.f.: (8 - 505*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.

A332148 a(n) = 4*(10^(2*n+1)-1)/9 + 4*10^n.

Original entry on oeis.org

8, 484, 44844, 4448444, 444484444, 44444844444, 4444448444444, 444444484444444, 44444444844444444, 4444444448444444444, 444444444484444444444, 44444444444844444444444, 4444444444448444444444444, 444444444444484444444444444, 44444444444444844444444444444, 4444444444444448444444444444444
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. A332118 .. A332178, A181965 (variants with different repeated digit 1, ..., 9).
Cf. A332140 .. A332149 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332148 := n -> 4*((10^(2*n+1)-1)/9+10^n);
  • Mathematica
    Array[4 ((10^(2 # + 1)-1)/9 + 10^#) &, 15, 0]
  • PARI
    apply( {A332148(n)=(10^(n*2+1)\9+10^n)*4}, [0..15])
  • Python
    def A332148(n): return (10**(n*2+1)//9+10**n)*4

Formula

a(n) = 4*A138148(n) + 8*10^n = A002278(2n+1) + 4*10^n = 4*A332112(n).
G.f.: (8 - 404*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.

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.

A332168 a(n) = 6*(10^(2*n+1)-1)/9 + 2*10^n.

Original entry on oeis.org

8, 686, 66866, 6668666, 666686666, 66666866666, 6666668666666, 666666686666666, 66666666866666666, 6666666668666666666, 666666666686666666666, 66666666666866666666666, 6666666666668666666666666, 666666666666686666666666666, 66666666666666866666666666666, 6666666666666668666666666666666
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. A332118 .. A332178, A181965 (variants with different repeated digit 1, ..., 9).
Cf. A332160 .. A332169 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332168 := n -> 6*(10^(2*n+1)-1)/9+2*10^n;
  • Mathematica
    Array[6 (10^(2 # + 1)-1)/9 + 2*10^# &, 15, 0]
Table[FromDigits[Join[PadRight[{},n,6],{8},PadRight[{},n,6]]],{n,0,20}] (* Harvey P. Dale, Oct 04 2021 *)
  • PARI
    apply( {A332168(n)=10^(n*2+1)\9*6+2*10^n}, [0..15])
  • Python
    def A332168(n): return 10**(n*2+1)//9*6+2*10**n

Formula

a(n) = 6*A138148(n) + 8*10^n = A002280(2n+1) + 2*10^n = 2*A332134(n).
G.f.: (8 - 202*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.
Showing 1-7 of 7 results.

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

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