A096845 Numbers n for which 4*R_n - 1 is a prime, where R_n = 11...1 is the repunit (A002275) of length n.

1, 2, 3, 6, 9, 12, 30, 32, 183, 297, 492, 41316

Offset: 1

Author

Labos Elemer, Jul 15 2004

Keywords

• hard
• more
• nonn

Comments

Also numbers n such that (4*10^n-13)/9 is prime.

a(13) > 10^5. - Robert Price, Oct 25 2014

Examples

			n=30 means that 444444444444444444444444444443 is prime.
		

Links

• Makoto Kamada, Prime numbers of the form 44...443.
• Index entries for primes involving repunits

Crossrefs

Cf. A096503-A096508, A096841-A096846, A000203, A056661.

Programs

Mathematica

Do[ If[ PrimeQ[ 4(10^n - 1)/9 - 1], Print[n]], {n, 5000}] (* Robert G. Wilson v, Oct 14 2004 *)
Select[Range[500],PrimeQ[FromDigits[PadLeft[{3},#,4]]]&] (* The program generates the first 11 terms of the sequence. *) (* Harvey P. Dale, Feb 10 2022 *)

Formula

a(n) = A056661(n) + 1.

Extensions

a(12) from Robert Price, Oct 25 2014