A099005 Numbers k such that 4*10^k + 6*R_k - 3 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

1, 2, 3, 4, 6, 7, 8, 12, 23, 59, 75, 144, 204, 268, 760, 1216, 1430, 1506, 1509, 2804, 2924, 3201, 3305, 5753, 9268, 11279, 19677, 23414, 28627, 31362, 42299, 49119, 63747, 81767, 111443, 263720, 264791

Offset: 1

Author

Julien Peter Benney (jpbenney(AT)ftml.net), Nov 07 2004

Keywords

• more
• nonn

Comments

Also numbers k such that (14*10^k - 11)/3 is a prime number.

a(38) > 3*10^5. - Robert Price, Mar 30 2015

Examples

			For n = 1, 2, 3, 4, 6, 7, 8 are members since 43, 463, 4663, 46663, 4666663, 46666663 and 466666663 are primes.
		

Links

• Makoto Kamada, Prime numbers of the form 466...663.
• Index entries for primes involving repunits.

Crossrefs

Cf. A101730.

Programs

Mathematica

Do[ If[ PrimeQ[(14*10^n - 11)/3], Print[n]], {n, 0, 10000}] (* Robert G. Wilson v, Dec 17 2004 *)

Formula

a(n) = A101730(n) + 1.

Extensions

a(15) - a(21) from Robert G. Wilson v, Dec 22 2004

a(22) - a(25) from Robert G. Wilson v, Jan 17 2005

a(26)-a(27) from Kamada link by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

a(28)-a(29) from Kamada data by Robert Price, Dec 08 2010

a(30)-a(32) from Erik Branger, May 01 2013, submitted by Ray Chandler, Aug 16 2013

a(33)-a(34) from Kamada data by Robert Price, Mar 30 2015

a(35)-a(37) from Robert Price, May 31 2023