A056704 Numbers k such that 3*10^k + 1*R_k is prime, where R_k = 11...1 is the repunit (A002275) of length k.

0, 1, 2, 5, 10, 11, 13, 34, 47, 52, 77, 88, 554, 580, 1310, 1505, 8537, 15892, 24022, 27041, 37922, 40033, 134122, 165358, 183760

Offset: 1

Author

Robert G. Wilson v, Aug 10 2000

Keywords

• hard
• nonn

Comments

Also numbers k such that (28*10^k - 1)/9 is prime.

Although perhaps a degenerate case, A002275 defines R(0)=0. Thus zero belongs in this sequence since 3*10^0 + 0 = 3*1 + 0 = 3 is prime. - Robert Price, Oct 28 2014

a(26) > 2*10^5. - Robert Price, Dec 19 2014

Links

• Makoto Kamada, Prime numbers of the form 311...11.
• Index entries for primes involving repunits

Crossrefs

Cf. A002275, A068813.

Programs

Mathematica

Do[ If[ PrimeQ[ 3*10^n + (10^n-1)/9], Print[n]], {n, 0, 10000}]

Extensions

Added zero by Robert Price, Oct 28 2014

a(18)-a(25) from Kamada data by Robert Price, Dec 19 2014