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.

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A093404 Primes of the form 70*R_k + 9, where R_k is the repunit (A002275) of length k.

Original entry on oeis.org

79, 777777777777777777777777777777777777777777777777777777777777777779, 77777777777777777777777777777777777777777777777777777777777777777777777777777777777779, 777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779
Offset: 1

Views

Author

Rick L. Shepherd, Mar 28 2004

Keywords

Comments

Primes of the form (7*10^k + 11)/9. - Vincenzo Librandi, Nov 16 2010

Crossrefs

Cf. A002275, A056693 (corresponding k), A098089.

Programs

  • Mathematica
    Select[Table[FromDigits[PadLeft[{9},n,7]],{n,100}],PrimeQ] (* Harvey P. Dale, May 09 2012 *)

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
Showing 1-2 of 2 results.