A084832 Numbers k such that 2*R_k - 1 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

4, 18, 100, 121, 244, 546, 631, 1494, 2566, 8088, 262603, 282948, 359860

Offset: 1

Author

Jason Earls, Jun 05 2003

Keywords

• more
• nonn

Comments

Also numbers k such that (2*10^k-11)/9 is prime.

Larger values correspond to strong pseudoprimes.

a(11) > 10^5. - Robert Price, Sep 06 2014

Examples

			a(1) = 4 because 2*(10^4-1)/9-1 = 2221 is prime.
a(2) = 18 means that 222222222222222221 is prime.
		

Links

• Makoto Kamada, Prime numbers of the form 22...221.
• Index entries for primes involving repunits

Crossrefs

Cf. A084831, A096503-A096508, A096841-A096846, A002275, A056660.

Programs

Maple

select(t -> isprime(2*(10^t-1)/9-1),[$1..1000]); # Robert Israel, Sep 07 2014

Mathematica

Do[ If[ PrimeQ[2(10^n - 1)/9 - 1], Print[n]], {n, 0, 7000}] (* Robert G. Wilson v, Oct 14 2004; fixed by Derek Orr, Sep 06 2014 *)

PARI

for(n=1, 10^4, if(ispseudoprime(2*(10^n-1)/9-1), print1(n,", "))) \\ Derek Orr, Sep 06 2014

Python

from sympy import isprime
def afind(limit):
  n, twoRn = 1, 2
  for n in range(1, limit+1):
    if isprime(twoRn-1): print(n, end=", ")
    twoRn = 10*twoRn + 2
afind(700) # Michael S. Branicky, Apr 18 2021

Formula

a(n) = A056660(n) + 1.

Extensions

a(8) from Labos Elemer, Jul 15 2004

a(10) from Kamada data by Robert Price, Sep 06 2014

a(11)-a(13) from Kamada data by Tyler Busby, Apr 29 2024