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.

A098089 Numbers k such that 7*R_k + 2 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

Original entry on oeis.org

0, 2, 66, 86, 90, 102, 386, 624, 7784, 18536, 113757, 135879
Offset: 1

Views

Author

Julien Peter Benney (jpbenney(AT)ftml.net), Sep 14 2004

Keywords

Comments

Also numbers k such that (7*10^k + 11)/9 is prime.
Although perhaps a degenerate case, A002275 defines R(0)=0. Thus zero belongs in this sequence since 7*0 + 2 = 2 is prime. - Robert Price, Oct 28 2014
a(11) > 10^5. - Robert Price, Nov 22 2014
a(13) > 2*10^5. - Tyler Busby, Feb 01 2023

Examples

			If k = 2, we get (7*10^2 + 11)/9 = (700+11)/9 = 79, which is prime.
		

Crossrefs

Programs

  • Magma
    [n: n in [0..300] |  IsPrime((7*10^n+11) div 9)]; // Vincenzo Librandi, Nov 22 2014
  • Mathematica
    Do[ If[ PrimeQ[ 7(10^n - 1)/9 + 2], Print[n]], {n, 0, 5000}] (* Robert G. Wilson v, Oct 15 2004 *)
    Do[ If[ PrimeQ[((7*10^n) + 11)/9], Print[n]], {n, 0, 8131}] (* Robert G. Wilson v, Sep 27 2004 *)
    Select[Range[0, 700], PrimeQ[(7 10^# + 11) / 9] &] (* Vincenzo Librandi, Nov 22 2014 *)

Formula

a(n) = A056693(n-1) + 1 for n>1.

Extensions

a(9) from Kamada link by Ray Chandler, Dec 23 2010
a(1)=0 added and Mathematica programs adapted by Robert Price, Oct 28 2014
a(11)-a(12) from Tyler Busby, Feb 01 2023

A056693 Numbers k such that 70*R_k + 9 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

Original entry on oeis.org

1, 65, 85, 89, 101, 385, 623, 7783, 18535, 113756, 135878
Offset: 1

Views

Author

Robert G. Wilson v, Aug 10 2000

Keywords

Comments

Also numbers k such that (7*10^(k+1)+11)/9 is prime.
a(12) > 2*10^5. - Tyler Busby, Feb 01 2023

Crossrefs

Programs

  • Magma
    [n: n in [1..400] |  IsPrime((7*10^(n+1)+11) div 9)];  Vincenzo Librandi, Nov 22 2014
  • Mathematica
    Do[ If[ PrimeQ[70*(10^n - 1)/9 + 9], Print[n]], {n, 0, 5000}]
    Select[Range[700], PrimeQ[(7 10^(# + 1) + 11) / 9] &] (* Vincenzo Librandi, Nov 22 2014 *)

Formula

a(n) = A098089(n+1) - 1. - Robert Price, Nov 22 2014

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008
a(9) derived from A098089 by Robert Price, Nov 22 2014
a(10)-a(11) from Tyler Busby, Feb 01 2023

A173808 a(n) = (7*10^n + 11)/9 for n > 0.

Original entry on oeis.org

9, 79, 779, 7779, 77779, 777779, 7777779, 77777779, 777777779, 7777777779, 77777777779, 777777777779, 7777777777779, 77777777777779, 777777777777779, 7777777777777779, 77777777777777779, 777777777777777779, 7777777777777777779, 77777777777777777779, 777777777777777777779
Offset: 1

Views

Author

Vincenzo Librandi, Feb 25 2010

Keywords

Crossrefs

Cf. A093404.

Programs

  • Magma
    [(7*10^n+11)/9: n in [1..20]]; // Vincenzo Librandi Jul 05 2012
  • Mathematica
    CoefficientList[Series[(9-20*x)/((1-x)*(1-10*x)),{x,0,30}],x] (* Vincenzo Librandi, Jul 05 2012 *)
    LinearRecurrence[{11,-10},{9,79},30] (* or *) Table[10*FromDigits[PadRight[{},n,7]]+9,{n,0,30}] (* Harvey P. Dale, Dec 03 2024 *)

Formula

a(n) = 10*a(n-1) - 11 with n > 0, a(0)=2.
From Vincenzo Librandi, Jul 05 2012: (Start)
G.f.: x*(9-20*x)/((1-x)*(1-10*x)).
a(n) = 11*a(n-1) - 10*a(n-2) for n > 2. (End)
E.g.f.: exp(x)*(7*exp(9*x) + 11)/9 - 2. - Elmo R. Oliveira, Sep 09 2024
Showing 1-3 of 3 results.