A056654 Numbers k such that 10*R_k + 3 is prime, where R_k is the repunit (A002275) of length k.

0, 1, 2, 4, 8, 10, 23, 83, 220, 1313, 2951, 20015, 51053

Offset: 1

Author

Robert G. Wilson v, Aug 09 2000

Keywords

• hard
• nonn
• more

Comments

Also numbers k such that (10^(k+1)+17)/9 is prime.

a(14) > 10^5. - Robert Price, Nov 01 2014

Examples

			8 is a term because 111111113 is a prime.
		

Links

• Makoto Kamada, Prime numbers of the form 11...113.
• Index entries for primes involving repunits

Crossrefs

Cf. A093011 (corresponding primes), A097683.

Programs

Mathematica

Do[ If[ PrimeQ[ 10*(10^n - 1)/9 + 3 ], Print[ n ] ], {n, 0, 1350} ]

PARI

is(n)=ispseudoprime(10^n\9*10+3) \\ Charles R Greathouse IV, Nov 10 2021

Formula

a(n) = A097683(n+1) - 1. - Robert Price, Nov 01 2014

Extensions

a(11) (only a probable prime) from Rick L. Shepherd, Mar 14 2004

a(12)-a(13) derived from A097683 by Robert Price, Nov 01 2014