A097684 Numbers k such that (10^k - 1)/9 + 6 is prime.

1, 2, 4, 5, 8, 23, 29, 40, 131, 136, 215, 611, 767, 2153, 2576, 22973, 42689, 85712, 85864, 112067, 538508, 631715

Offset: 1

Author

Carl R. White, Aug 19 2004

Keywords

• nonn

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

• Makoto Kamada, Prime numbers of the form 11...117.
• Index entries for primes involving repunits

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