A183176 Numbers k such that (10^(2k+1) + 12*10^k - 1)/3 is prime.

1, 3, 7, 11, 13, 17, 29, 31, 33, 77, 933, 1555, 11758, 117707

Offset: 1

Author

Ray Chandler, Dec 28 2010

Keywords

• nonn
• more
• base

Comments

a(14) > 100000. - Robert Price, Dec 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...33733...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) + 12*10^n - 1)/3], Print[n]], {n, 3000}]

PARI

is(n)=ispseudoprime((10^(2*n+1)+12*10^n-1)/3) \\ Charles R Greathouse IV, Jun 13 2017

Formula

a(n) = (A077790(n) - 1)/2.

Extensions

a(14) from Robert Price, Oct 30 2023