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 1-2 of 2 results.

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

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.

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.

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.
Showing 1-2 of 2 results.