A096507 Numbers k such that 6*R_k + 1 is a prime, where R_k = 11...1 is the repunit (A002275) of length k.

1, 2, 6, 8, 9, 11, 20, 23, 41, 63, 66, 119, 122, 149, 252, 284, 305, 592, 746, 875, 1204, 1364, 2240, 2403, 5106, 5776, 5813, 12456, 14235, 39606, 55544, 84239, 275922

Offset: 1

Author

Labos Elemer, Jul 12 2004

Keywords

• nonn

Comments

Also numbers k such that (2*10^k + 1)/3 is prime.

These numbers form a near-repdigit sequence (6)w7.

All the terms from k = 2403 through 14235 correspond to primes. - Joao da Silva (zxawyh66(AT)yahoo.com), Oct 03 2005

Examples

			k = 9 gives 2000000001/3 = 666666667, which is prime.
k = 20 gives 66666666666666666667, which is prime.
		

Links

• Makoto Kamada, Prime numbers of the form 66...667.
• Index entries for primes involving repunits

Crossrefs

Cf. A002275, A056657, A093170, A096503, A096504, A096505, A096506, A096508.

Programs

Mathematica

Select[Range@ 2500, PrimeQ[FromDigits@ Table[6, {#}] + 1] &] (* or *)
Select[Range@ 2500, PrimeQ[2 (10^# - 1)/3 + 1] &] (* Michael De Vlieger, Jul 04 2016 *)

Formula

a(n) = A056657(n) + 1.

Extensions

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

39606 and 55544 from Serge Batalov, Jun 2009

84239 from Serge Batalov, Jul 06 2009 confirmed as next term by Ray Chandler, Feb 23 2012

a(33) from Kamada data by Tyler Busby, Apr 14 2024