A183174 Numbers k such that (10^(2k+1) - 6*10^k - 1)/3 is prime.

1, 3, 7, 61, 90, 92, 269, 298, 321, 371, 776, 1567, 2384, 2566, 3088, 5866, 8051, 9498, 12635, 24512, 32521, 43982

Offset: 1

Author

Ray Chandler, Dec 28 2010

Keywords

• nonn
• base

Comments

a(23) > 10^5. - Robert Price, Jan 29 2016

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 33...33133...33.
• Index entries for primes involving repunits.

Crossrefs

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

Programs

Mathematica

Do[If[PrimeQ[(10^(2n + 1) - 6*10^n - 1)/3], Print[n]], {n, 3000}]

PARI

for(n=1,1e3,if(ispseudoprime((10^(2*n+1)-6*10^n-1)/3),print1(n", "))) \\ Charles R Greathouse IV, Jul 15 2011

Formula

a(n) = (A077775(n) - 1)/2.

Extensions

a(21)-a(22) from Robert Price, Jan 29 2016