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.

A097683 Numbers k such that R_k + 2 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

Original entry on oeis.org

0, 1, 2, 3, 5, 9, 11, 24, 84, 221, 1314, 2952, 20016, 51054
Offset: 1

Views

Author

Carl R. White and Julien Peter Benney (jpbenney(AT)ftml.net), Aug 19 2004

Keywords

Comments

Also numbers k such that (10^k + 17)/9 is prime.
The corresponding values R_k + 2 are primes of the form "(n-1) ones followed by a three"; zero is a degenerate case. Related to the base-10 repunit primes.
a(15) > 10^5. - Robert Price, Oct 12 2014
By Kamada link, a(15) > 4*10^5. - Jeppe Stig Nielsen, Jan 17 2023

Examples

			11113 = ((10^5)+17)/9 and 11113 is prime.

Links

Crossrefs

Cf. A002275, A004023, A056654, A097684, A097685.

Programs

  • Maple
    A097683:=n->`if`((10^n+17 mod 9) = 0 and isprime(floor((10^n+17)/9)),n,NULL): seq(A097683(n), n=0..10^3); # Wesley Ivan Hurt, Oct 12 2014
  • Mathematica
    Do[ If[ PrimeQ[(10^n - 1)/9 + 2], Print[n]], {n, 0, 5951}] (* Robert G. Wilson v, Oct 15 2004 *)

Formula

a(n) = A056654(n-1) + 1.

Extensions

a(11)-a(12) from Robert G. Wilson v, Oct 15 2004
Edited by N. J. A. Sloane, Apr 02 2009, at the suggestion of Farideh Firoozbakht
a(13) from Kamada link by Ray Chandler, Dec 23 2010
a(14) from Robert Price, Oct 12 2014

A097684 Numbers k such that (10^k - 1)/9 + 6 is prime.

Original entry on oeis.org

1, 2, 4, 5, 8, 23, 29, 40, 131, 136, 215, 611, 767, 2153, 2576, 22973, 42689, 85712, 85864, 112067, 538508, 631715
Offset: 1

Views

Author

Carl R. White, Aug 19 2004

Keywords

Comments

Values indicate primes of the form "(k-1) ones followed by a seven". Related to the base-10 repunit primes.
Some of the larger entries may only correspond to probable primes.
a(20) > 10^5. - Robert Price, Jan 11 2015
Corresponding primes are equal to (10^k + 53)/9. - Robert Price, Jan 11 2015
a(23) > 6.7*10^5, determined by Rytis Slatkevičius. - Jeppe Stig Nielsen, Jan 20 2023

Links

Crossrefs

Cf. A004023, A056655, A097683, A097685.

Programs

  • Mathematica
    Do[ If[ PrimeQ[(10^n - 1)/9 + 6], Print[n]], {n, 0, 5000}] (* Robert G. Wilson v, Oct 14 2004 *)
  • PARI
    for (i=1,1000,if(isprime((10^i-1)/9 + 6),print1(i,","))) \\ Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), Aug 23 2004

Formula

a(n) = A056655(n) + 1 for all n >= 0.

Extensions

a(12)-a(13) from Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), Aug 23 2004
a(12)-a(15) from Rick L. Shepherd, Aug 23 2004
a(16)-a(19) from Robert Price, Jan 11 2015
a(20) from Serge Batalov and a(21)-a(22) from Rytis Slatkevičius communicated by Jeppe Stig Nielsen, Jan 20 2023

A056659 Numbers k such that 10*R_k + 9 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

Original entry on oeis.org

1, 4, 5, 7, 16, 49, 683, 719, 1451, 1678, 3145, 72820
Offset: 1

Views

Author

Robert G. Wilson v, Aug 09 2000

Keywords

Comments

Also numbers k such that (10^(k+1)+71)/9 is prime.
a(13) > 10^5. - Robert Price, Nov 01 2014

Links

Crossrefs

Cf. A002275, A097685.

Programs

  • Mathematica
    Do[ If[ PrimeQ[10*(10^n - 1)/9 + 9], Print[n]], {n, 5000}]

Formula

a(n) = A097685(n) - 1. - Robert Price, Nov 01 2014

Extensions

a(12) derived from A097685 by Robert Price, Nov 01 2014
Showing 1-3 of 3 results.

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

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