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 1-6 of 6 results.

A056654 Numbers k such that 10*R_k + 3 is prime, where R_k is the repunit (A002275) of length k.

Original entry on oeis.org

0, 1, 2, 4, 8, 10, 23, 83, 220, 1313, 2951, 20015, 51053
Offset: 1

Views

Author

Robert G. Wilson v, Aug 09 2000

Keywords

Comments

Also numbers k such that (10^(k+1)+17)/9 is prime.
a(14) > 10^5. - Robert Price, Nov 01 2014

Examples

			8 is a term because 111111113 is a prime.

Links

Crossrefs

Cf. A093011 (corresponding primes), A097683.

Programs

  • Mathematica
    Do[ If[ PrimeQ[ 10*(10^n - 1)/9 + 3 ], Print[ n ] ], {n, 0, 1350} ]
  • PARI
    is(n)=ispseudoprime(10^n\9*10+3) \\ Charles R Greathouse IV, Nov 10 2021

Formula

a(n) = A097683(n+1) - 1. - Robert Price, Nov 01 2014

Extensions

a(11) (only a probable prime) from Rick L. Shepherd, Mar 14 2004
a(12)-a(13) derived from A097683 by Robert Price, Nov 01 2014

A098406 a(n) = (10^n + 17)/9.

Original entry on oeis.org

2, 3, 13, 113, 1113, 11113, 111113, 1111113, 11111113, 111111113, 1111111113, 11111111113, 111111111113, 1111111111113, 11111111111113, 111111111111113, 1111111111111113, 11111111111111113, 111111111111111113, 1111111111111111113, 11111111111111111113, 111111111111111111113
Offset: 0

Views

Author

Klaus Brockhaus, Sep 07 2004

Keywords

Comments

A097683 gives numbers k such that a(k) is prime.

Examples

			a(5) = (100000 + 17)/9 = 11113.

Links

Crossrefs

Cf. A097683, A047855, A002275.
Cf. A002282, A062397.

Programs

  • Mathematica
    FromDigits/@Table[PadLeft[{3},n,1],{n,20}] (* Harvey P. Dale, Jun 18 2011 *)
  • PARI
    for(n=1,18,print1(((10^n)+17)/9,","))

Formula

a(1) = 3; a(n) = a(n-1) + 10^(n-1).
a(1) = 3; a(n) = 10*a(n-1) - 17.
a(n) = A047855(n)+1 = A002275(n)+2.
G.f.: (2-19*x)/((10*x-1)*(x-1)). - R. J. Mathar, Jan 27 2017
From Elmo R. Oliveira, Aug 23 2024: (Start)
E.g.f.: exp(x)*(exp(9*x) + 17)/9.
a(n) = A062397(n) - A002282(n).
a(n) = 11*a(n-1) - 10*a(n-2) for n > 1. (End)

Extensions

a(0) from Ivan Panchenko, Nov 02 2013

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

A097685 Numbers k such that R_k + 8 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

Original entry on oeis.org

2, 5, 6, 8, 17, 50, 684, 720, 1452, 1679, 3146, 72821, 111902, 146063, 180689, 330906
Offset: 1

Views

Author

Carl R. White, Aug 19 2004

Keywords

Comments

Also numbers k such that (10^k + 71)/9 is prime.
The corresponding values R_k + 8 are primes of the form "(k-1) ones followed by a nine". Related to the base-10 repunit primes.
a(13) > 10^5. - Robert Price, Nov 01 2014

Links

Crossrefs

Cf. A004023, A056659, A097683, A097684.

Programs

  • Mathematica
    Do[ If[ PrimeQ[(10^n - 1)/9 + 8], Print[n]], {n, 0, 5000}] (* Robert G. Wilson v, Oct 14 2004 *)

Formula

a(n) = A056659(n) + 1.

Extensions

a(12) from Robert Price, Nov 01 2014
a(13)-a(16) from Kamada data by Tyler Busby, May 03 2024

A105432 Numbers n such that the near-repdigit number consisting of n-1 1's followed by a terminal 3 (i.e., of the form 111...1113) is composite.

Original entry on oeis.org

4, 6, 7, 8, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78
Offset: 1

Views

Author

Lekraj Beedassy, Apr 08 2005

Keywords

Comments

Complement of A097683.
Numbers k such that (10^n + 17)/9 is composite (see A098406).

Links

Crossrefs

Cf. A098406, A105433.

Programs

  • Mathematica
    IntegerLength/@Select[Table[FromDigits[PadLeft[{3},n,1]],{n,80}],CompositeQ] (* Harvey P. Dale, Feb 05 2025 *)
  • PARI
    isok(n) = ! isprime((10^n + 17)/9); \\ Michel Marcus, Jul 27 2017

A105431 Primes of form R_n + 2 {= (10^n + 17)/9}, R_n being the n-th repunit, i.e., primes consisting of a string of 1's followed by a terminal 3.

Original entry on oeis.org

3, 13, 113, 1113, 111113, 1111111113, 111111111113, 1111111111111111111111113, 1111111111111111111111111111111111111111111111111111111111111111111111111111111111113
Offset: 1

Views

Author

Lekraj Beedassy, Apr 08 2005

Keywords

Comments

For the associated positive values n see A097683.

Links

Crossrefs

Cf. A098406.
Showing 1-6 of 6 results.

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