A056657 Numbers k such that 60*R_k + 7 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

0, 1, 5, 7, 8, 10, 19, 22, 40, 62, 65, 118, 121, 148, 251, 283, 304, 591, 745, 874, 1203, 1363, 2239, 2402, 5105, 5775, 5812, 12455, 14234, 39605, 55543, 84238, 275921

Offset: 1

Author

Robert G. Wilson v, Aug 09 2000

Keywords

• nonn

Comments

Also numbers k such that (20*10^k+1)/3 is prime.

Examples

			7, 67, 666667, 66666667, 666666667, 66666666667, etc. are primes.
		

Links

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

Crossrefs

Cf. A002275, A093170, A096507.

Programs

Mathematica

Do[ If[ PrimeQ[ 60*(10^n - 1)/9 + 7 ], Print[n]], {n, 25556}]

Formula

a(n) = A096507(n) - 1.

Extensions

More terms from Robert G. Wilson v, Oct 22 2003

2239,2402,5105,5775 from Farideh Firoozbakht, Dec 23 2003

39605 and 55543 from Serge Batalov, Jun 2009

84238 from Serge Batalov, Jul 06 2009 confirmed as next term by Ray Chandler, Feb 23 2012

a(33) derived from A096507 by Robert Price, Jul 07 2024