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 1-4 of 4 results.

A096846 Numbers n for which 8*R_n - 1 is prime, where R_n = 11...1 is the repunit (A002275) of length n.

Original entry on oeis.org

1, 3, 4, 6, 9, 12, 72, 118, 124, 190, 244, 304, 357, 1422, 2691, 5538, 7581, 21906, 32176, 44358, 120552, 137073, 152260
Offset: 1

Views

Author

Labos Elemer, Jul 15 2004

Keywords

Comments

Also numbers n such that (8*10^n-17)/9 is prime.
The numbers corresponding to a(1)-a(15) are certified prime, the numbers corresponding to a(16)-a(20) are probable primes. a(21) > 10^5. - Robert Price, May 20 2014

Examples

			n=6: a(4)=888887 which is prime.
		

Crossrefs

Programs

  • Mathematica
    Do[ If[ PrimeQ[ 8(10^n - 1)/9 - 1], Print[n]], {n, 0, 5000}] (* Robert G. Wilson v, Oct 15 2004; corrected by Derek Orr, Sep 06 2014 *)
  • PARI
    for(n=1,10^4,if(ispseudoprime(8*(10^n-1)/9-1),print1(n,", "))) \\ Derek Orr, Sep 06 2014

Formula

a(n) = A056695(n) + 1. - Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008
a(18)-a(20) discovered and reported to Makoto Kamada by Erik Branger; added to OEIS by Robert Price, May 20 2014
a(21)-a(23) from Kamada data by Tyler Busby, Apr 23 2024

A173812 a(n) = (8*10^n - 17)/9 for n > 0.

Original entry on oeis.org

7, 87, 887, 8887, 88887, 888887, 8888887, 88888887, 888888887, 8888888887, 88888888887, 888888888887, 8888888888887, 88888888888887, 888888888888887, 8888888888888887, 88888888888888887, 888888888888888887, 8888888888888888887, 88888888888888888887, 888888888888888888887
Offset: 1

Views

Author

Vincenzo Librandi, Feb 25 2010

Keywords

Crossrefs

Cf. A093171.

Programs

  • Magma
    [(8*10^n-17)/9: n in [1..20]]; // Vincenzo Librandi, Jul 05 2012
  • Mathematica
    CoefficientList[Series[(7+10*x)/((1-x)*(1-10*x)),{x,0,30}],x] (* Vincenzo Librandi, Jul 05 2012 *)
    Table[FromDigits[PadLeft[{7},n,8]],{n,20}] (* Harvey P. Dale, Jun 22 2013 *)

Formula

a(n) = 10*a(n-1) + 17 with n > 0, a(0)=-1.
From Vincenzo Librandi, Jul 05 2012: (Start)
a(n) = 11*a(n-1) - 10*a(n-2) for n > 2.
G.f.: x*(7+10*x)/((1-x)*(1-10*x)). (End)
E.g.f.: 1 + exp(x)*(8*exp(9*x) - 17)/9. - Elmo R. Oliveira, Sep 09 2024

A056695 Numbers k such that 80*R_k + 7 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

Original entry on oeis.org

0, 2, 3, 5, 8, 11, 71, 117, 123, 189, 243, 303, 356, 1421, 2690, 5537, 7580, 21905, 32175, 44357
Offset: 1

Views

Author

Robert G. Wilson v, Aug 10 2000

Keywords

Comments

Also numbers k such that (8*10^(k+1)-17)/9 is prime.
a(21) > 10^5. - Robert Price, May 20 2014

Crossrefs

Programs

  • Mathematica
    Do[ If[ PrimeQ[80*(10^n - 1)/9 + 7], Print[n]], {n, 0, 5000}]

Formula

a(n) = A096846(n) - 1.

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008
a(18)-a(20) derived from A096846 by Robert Price, May 20 2014

A096843 Primes of form repdigit - 1. Primes whose sum of divisors is a decimal repdigit.

Original entry on oeis.org

2, 3, 5, 7, 43, 443, 887, 2221, 8887, 444443, 888887, 444444443, 888888887, 444444444443, 888888888887, 222222222222222221, 444444444444444444444444444443, 44444444444444444444444444444443
Offset: 1

Views

Author

Labos Elemer, Jul 15 2004

Keywords

Comments

Union numbers 2, 5 and sequences A093171, A093163 and A091189.
Corresponding values of sigma(a(n)) are in A028987. - Jaroslav Krizek, Mar 19 2013

Examples

			n=43: sigma(43)=44;
		

Crossrefs

Extensions

Missing a(1)=2 and a(3)=5 added by Jaroslav Krizek, Mar 19 2013
Showing 1-4 of 4 results.