A056725 Numbers k such that 9*10^k - 1 is prime.

1, 3, 7, 19, 29, 37, 93, 935, 8415, 9631, 11143, 41475, 41917, 48051, 107663, 212903, 223871, 260253, 364521, 383643, 1009567, 1762063

Offset: 1

Author

Robert G. Wilson v, Aug 11 2000

Keywords

• hard
• nonn
• more

Comments

Also numbers k such that 8*10^k + 9*R_k is prime, where R_k = 11...1 is the repunit (A002275) of length k.

1009567 is also a member of this sequence, but its position is presently undetermined: 9 * 10^1009567 - 1 is prime. - Predrag Kurtovic, Sep 19 2016

Links

• Makoto Kamada, Prime numbers of the form 899...999.
• Index entries for primes involving repunits

Crossrefs

Cf. A003307, A002235, A046865, A079906, A046866, A001771, A005541, A046867, A079907.

Programs

Mathematica

Do[ If[ PrimeQ[ 8*10^n + (10^n-1)], Print[n]], {n, 1, 6750, 2}]

PARI

is(n)=isprime(9*10^n-1) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

a(16)-a(20) from Kamada data by Robert Price, Oct 19 2014

a(21) from Kamada data by Robert Price, Mar 10 2019

a(22) from Kamada data by Mohammed Yaseen, Jul 18 2021