A098088 Numbers k such that 6*R_k - 5 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

2, 3, 4, 10, 18, 21, 22, 28, 43, 66, 121, 133, 178, 241, 454, 553, 1600, 2175, 2978, 3649, 7708, 8316, 10392, 12458, 21057, 26223, 48297, 64041, 84904, 92976, 95072, 103161, 140461, 141751, 150612, 265321, 672745

Offset: 1

Author

Julien Peter Benney (jpbenney(AT)ftml.net), Sep 14 2004

Keywords

• more
• nonn
• changed

Comments

Also numbers k such that (2*10^k - 17)/3 is prime.

The terms 1600, 2175, 2978 and 3649 correspond to primes. - Joao da Silva (zxawyh66(AT)yahoo.com), Oct 03 2005

a(37) > 3*10^5, Robert Price, Oct 19 2023

Examples

			If n = 4 we get ((2*10^4)-17)/3 = 19983/3 = 6661, which is prime.
		

Links

• Makoto Kamada, Prime numbers of the form 66...661.
• Index entries for primes involving repunits

Programs

Mathematica

Do[ If[ PrimeQ[ 2(10^n - 1)/3 - 5], Print[n]], {n, 0, 7000}]

Formula

a(n) = A056658(n) + 1. - Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

Extensions

a(21)-a(22) from Kamada link by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

a(23)-a(26) from Kamada link by Ray Chandler, Dec 23 2010

a(27) from Kamada link by Robert Price, Aug 17 2014

a(28)-a(31) from Robert Price, Aug 17 2014

a(32)-a(36) from Robert Price, Oct 19 2023

a(37) from Kamada link by Tyler Busby, Sep 04 2025