A102975 Numbers k such that 3*10^k + 6*R_k + 1 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

1, 2, 12, 15, 51, 194, 498, 2136, 2822, 3762, 7428, 22740, 30452, 37952, 55254

Offset: 1

Author

Robert G. Wilson v, Dec 17 2004

Keywords

• more
• nonn

Comments

Also numbers k such that (11*10^k+1)/3 is prime.

a(16) > 10^5. - Robert Price, Jan 29 2015

Links

• Makoto Kamada, Prime numbers of the form 366...667.
• Index entries for primes involving repunits.

Crossrefs

Cf. A002275, A101840.

Programs

Magma

[n: n in [0..300] | IsPrime((11*10^n+1) div 3)]; // Vincenzo Librandi, Dec 01 2015

Mathematica

Do[ If[ PrimeQ[(11*10^n+1)/3], Print[n]], {n, 0, 10000}]

Formula

a(n) = A101840(n) + 1.

Extensions

Addition of a(12) from Kamada data by Robert Price, Dec 13 2010

a(13)-a(14) from Erik Branger May 01 2013 by Ray Chandler, Aug 16 2013

a(15) from Kamada data by Robert Price, Jan 29 2015