A183187 Numbers k such that 10^(2k+1)-10^k-1 is prime.

26, 378, 1246, 1798, 2917, 23034, 47509, 52140, 67404

Offset: 1

Author

Ray Chandler, Dec 28 2010

Keywords

• nonn
• more
• base

Comments

944264 is a term but its position is not known. - Jeppe Stig Nielsen, Jan 12 2024

a(10) > 300000. - Serge Batalov, Jan 17 2024

References

• C. Caldwell and H. Dubner, "Journal of Recreational Mathematics", Volume 28, No. 1, 1996-97, pp. 1-9.

Links

• Patrick De Geest, World!Of Numbers, Palindromic Wing Primes (PWP's)
• Makoto Kamada, Prime numbers of the form 99...99899...99
• PrimePages, Database Search Output.
• Index entries for primes involving repunits.

Crossrefs

Cf. A004023, A077775-A077798, especially A077794, A107123-A107127, A107648, A107649, A115073, A183174-A183187.

Programs

Mathematica

Do[If[PrimeQ[10^(2n + 1) - 10^n - 1], Print[n]], {n, 3000}]

PARI

for(n=1,1e3,if(ispseudoprime(10^(2*n+1)-10^n-1),print1(n", "))) \\ Charles R Greathouse IV, Jul 15 2011

Formula

a(n) = (A077794(n)-1)/2.