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.

A057678 Primes of the form 2^p - p where p is prime.

Original entry on oeis.org

2, 5, 8179, 524269
Offset: 1

Views

Author

Labos Elemer, Oct 19 2000

Keywords

Comments

Next term, if it exists, has more than 618 digits. - Emeric Deutsch, Mar 27 2005
Next term, if it exists, has more than 10,000 digits.
The corresponding primes p are: 2, 3, 13, 19, .... - Gerasimov Sergey, Jul 26 2013
The corresponding 2^p - 1 are 3, 7, 8191, 524287 which are Mersenne primes (A000668). Is this the case for all members of the sequence? None of the other Mersenne primes < 2^132049-1 correspond to members of the sequence. - Robert Israel, Jul 18 2016
Next term is 2^481801-481801. 2^481801-1 is not a Mersenne prime. - Joerg Arndt, Jul 19 2016

Examples

			p=3 is prime, and so is 2^p - p = 8 - 3 = 5, so 5 is in the sequence. - _Michael B. Porter_, Jul 19 2016
		

Crossrefs

Programs

  • Maple
    a:=proc(n) if isprime(2^ithprime(n)-ithprime(n))=true then 2^ithprime(n)-ithprime(n) else fi end: seq(a(n),n=1..310); # Emeric Deutsch
  • Mathematica
    lst={};Do[p=Prime[n];If[PrimeQ[p=2^p-p],AppendTo[lst,p]],{n,5!}];lst (* Vladimir Joseph Stephan Orlovsky, Jan 28 2009 *)
    Select[Table[2^p-p,{p,Prime[Range[20]]}],PrimeQ] (* Harvey P. Dale, Sep 20 2018 *)

A099409 Numbers k such that 2*R_k + 5 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

Original entry on oeis.org

0, 1, 3, 9, 15, 28, 64, 1168, 1695, 2362, 116620, 336405
Offset: 1

Views

Author

Robert G. Wilson v, Oct 14 2004

Keywords

Comments

Also numbers k such that (2*10^k + 43)/9 is prime.
a(11) > 50000. - Robert Price, Oct 27 2014

Crossrefs

Programs

  • Magma
    [n: n in [0..1000] | IsPrime( 2*(10^n - 1) div 9 + 5)]; // Vincenzo Librandi, Oct 28 2014
  • Mathematica
    Do[ If[ PrimeQ[ 2(10^n - 1)/9 + 5], Print[n]], {n, 0, 5000}]

Formula

a(n) = A056677(n-1) + 1.

Extensions

Added a(1)=0, adapted Mathematica program, Vincenzo Librandi, Oct 28 2014
a(11)-a(12) from Kamada data by Tyler Busby, May 03 2024

A093167 Primes of the form 20*R_k + 7, where R_k is the repunit (A002275) of length k.

Original entry on oeis.org

7, 227, 222222227, 222222222222227, 2222222222222222222222222227, 2222222222222222222222222222222222222222222222222222222222222227
Offset: 1

Views

Author

Rick L. Shepherd, Mar 26 2004

Keywords

Crossrefs

Cf. A002275, A056677 (corresponding k and count of digits 2 in a(n)), A099409.

Programs

  • Mathematica
    Select[FromDigits /@ NestList["2" <> # &, "7", 10^3], PrimeQ] (* Mikk Heidemaa, Nov 18 2015 *)
  • PARI
    list(lim)=for(i=0,lim,m=20*(10^i-1)/9 + 7;if(isprime(m),print1(m," ,"))) \\ Anders Hellström, Nov 18 2015
Showing 1-3 of 3 results.