A056714 Numbers k such that 5*10^k + 3*R_k is prime, where R_k = 11...1 is the repunit (A002275) of length k.

0, 1, 3, 13, 25, 49, 143, 419, 1705, 13993, 35753, 40889

Offset

1,3

Comments

Also numbers k such that (16*10^k - 1)/3 is prime.

5*10^a(n) + 3*(10^a(n) - 1)/9 is a solution for part (b) of questions of puzzle 244 from www.primepuzzles.net. If a(n) is greater than 5812 then a(n) is an example that is asked for in this question. - Farideh Firoozbakht, Dec 02 2003

Links

Table of n, a(n) for n=1..12.

Makoto Kamada, Prime numbers of the form 533...33.

Carlos Rivera, Puzzle 244. Null Conjunction, The Prime Puzzles and Problems Connection.

Index entries for primes involving repunits

Mathematica

Do[ If[ PrimeQ[ 5*10^n + 3*(10^n-1)/9], Print[n]], {n, 0, 5000}]

Crossrefs

Cf. A002275, A093674, A350995.

Sequence in context: A030552 A146371 A146379 * A120074 A056706 A052454

Adjacent sequences: A056711 A056712 A056713 * A056715 A056716 A056717

Keyword

nonn

Author

Robert G. Wilson v, Aug 11 2000

Extensions

1705 from Farideh Firoozbakht, Dec 18 2003

13993, 35753 and 40889 from Serge Batalov, Jan 2009 confirmed as next terms by Ray Chandler, Feb 11 2012

Status

approved