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 1-3 of 3 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.

A332169 a(n) = 6*(10^(2*n+1)-1)/9 + 3*10^n.

Original entry on oeis.org

9, 696, 66966, 6669666, 666696666, 66666966666, 6666669666666, 666666696666666, 66666666966666666, 6666666669666666666, 666666666696666666666, 66666666666966666666666, 6666666666669666666666666, 666666666666696666666666666, 66666666666666966666666666666, 6666666666666669666666666666666
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. A332119 .. A332189 (variants with different repeated digit 1, ..., 8).
Cf. A332160 .. A332169 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332169 := 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( {A332169(n)=10^(n*2+1)\9*6+3*10^n}, [0..15])
  • Python
    def A332169(n): return 10**(n*2+1)//9*6+3*10**n

Formula

a(n) = 6*A138148(n) + 9*10^n = A002280(2n+1) + 3*10^n = 3*A332123(n).
G.f.: (9 - 303*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.

A332146 a(n) = 4*(10^(2*n+1)-1)/9 + 2*10^n.

Original entry on oeis.org

6, 464, 44644, 4446444, 444464444, 44444644444, 4444446444444, 444444464444444, 44444444644444444, 4444444446444444444, 444444444464444444444, 44444444444644444444444, 4444444444446444444444444, 444444444444464444444444444, 44444444444444644444444444444, 4444444444444446444444444444444
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. A332116 .. A332196 (variants with different repeated digit 2, ..., 9).
Cf. A332140 .. A332149 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332146 := n -> 4*(10^(2*n+1)-1)/9+2*10^n;
  • Mathematica
    Array[4 (10^(2 # + 1)-1)/9 + 2*10^# &, 15, 0]
  • PARI
    apply( {A332146(n)=10^(n*2+1)\9*4+2*10^n}, [0..15])
  • Python
    def A332146(n): return 10**(n*2+1)//9*4+2*10**n

Formula

a(n) = 4*A138148(n) + 6*10^n = A002278(2n+1) + 2*10^n = 2*A332123(n).
G.f.: (6 - 202*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 1-3 of 3 results.

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

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