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.

A099422 Numbers k such that 8*R_k - 5 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

Original entry on oeis.org

1, 2, 3, 5, 8, 9, 15, 51, 71, 77, 224, 296, 315, 2090, 2906, 3395, 3882, 5114, 6056, 7254, 7995, 18173, 18971, 35006, 69674, 175428, 253313
Offset: 1

Views

Author

Robert G. Wilson v, Oct 14 2004

Keywords

Comments

Also numbers k >= 1 such that (8*10^k - 53)/9 is prime.
a(26) > 10^5. - Robert Price, Oct 31 2014

Links

Crossrefs

Cf. A002275, A056664, A056694, A093166.

Programs

  • Magma
    [n: n in [1..500] | IsPrime((8*10^n-53) div 9)]; // Vincenzo Librandi, Nov 01 2014
  • Mathematica
    Do[ If[ PrimeQ[ 8(10^n - 1)/9 - 5], Print[n]], {n, 1, 5000}]

Formula

a(n) = A056694(n) + 1.

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008
a(22)-a(25) from Robert Price, Oct 31 2014
a(1)=0 removed by Georg Fischer, Jan 03 2021
a(26)-a(27) from Kamada data by Tyler Busby, Apr 16 2024

A056694 Numbers k such that 80*R_k + 3 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

Original entry on oeis.org

0, 1, 2, 4, 7, 8, 14, 50, 70, 76, 223, 295, 314, 2089, 2905, 3394, 3881, 5113, 6055, 7253, 7994, 18172, 18970, 35005, 69673
Offset: 1

Views

Author

Robert G. Wilson v, Aug 10 2000

Keywords

Comments

Also numbers k such that (8*10^(k+1)-53)/9 is prime.
a(26) > 10^5. - Robert Price, Oct 31 2014

Links

Crossrefs

Cf. A002275, A093166, A099422.

Programs

  • Magma
    [n: n in [0..500] | IsPrime((8*10^(n+1)-53) div 9)]; // Vincenzo Librandi, Nov 01 2014
  • Mathematica
    Do[ If[ PrimeQ[80*(10^n - 1)/9 + 3], Print[n]], {n, 0, 5000}]

Formula

a(n) = A099422(n) - 1. [adapted by Georg Fischer, Jan 04 2021]

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008
a(22)-a(25) from Robert Price, Oct 31 2014

A173811 a(n) = (8*10^n - 53)/9 for n > 0.

Original entry on oeis.org

3, 83, 883, 8883, 88883, 888883, 8888883, 88888883, 888888883, 8888888883, 88888888883, 888888888883, 8888888888883, 88888888888883, 888888888888883, 8888888888888883, 88888888888888883, 888888888888888883, 8888888888888888883, 88888888888888888883, 888888888888888888883
Offset: 1

Views

Author

Vincenzo Librandi, Feb 25 2010

Keywords

Links

Crossrefs

Cf. A093166.

Programs

  • Magma
    [(8*10^n-53)/9: n in [1..20]]; // Vincenzo Librandi, Jul 05 2012
  • Mathematica
    NestList[10#+53&,3,20] (* Harvey P. Dale, Jun 13 2011 *)
CoefficientList[Series[(3+50*x)/((1-x)*(1-10*x)),{x,0,30}],x] (* Vincenzo Librandi, Jul 05 2012 *)

Formula

a(n) = 10*a(n-1) + 53 for n > 0, a(0) = -5.
From Vincenzo Librandi, Jul 05 2012: (Start)
G.f.: x*(3+50*x)/((1-x)*(1-10*x)).
a(n) = 11*a(n-1) - 10*a(n-2). (End)
E.g.f.: exp(x)*(8*exp(9*x) - 53)/9. - Elmo R. Oliveira, Sep 09 2024
Showing 1-3 of 3 results.

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

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