A099410 Numbers k such that 2*R_k + 7 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

0, 2, 3, 5, 14, 176, 416, 2505, 2759, 7925, 9401, 10391, 12105, 19616, 261704, 264539

Offset: 1

Author

Robert G. Wilson v, Oct 14 2004

Keywords

• nonn

Comments

Also numbers k such that (2*10^k + 61)/9 is prime.

Although perhaps a degenerate case, A002275 defines R(0)=0. Thus zero belongs in this sequence since 2*0+7=7 is prime. - Robert Price, Oct 28 2014

a(15) > 10^5. - Robert Price, Oct 29 2014

Links

• Makoto Kamada, Prime numbers of the form 22...229.
• Index entries for primes involving repunits

Crossrefs

Cf. A002275, A056678, A093401.

Programs

Magma

[n: n in [0..500] | IsPrime((2*10^n+61) div 9)]; // Vincenzo Librandi, Oct 30 2014

Mathematica

Do[ If[ PrimeQ[ 2(10^n - 1)/9 + 7], Print[n]], {n, 0, 5000}]

Formula

a(n) = A056678(n-1) + 1.

Extensions

Added zero and adapted Mathematica program by Robert Price, Oct 28 2014

a(10)-a(14) from Kamada data by Robert Price, Oct 29 2014

a(15)-a(16) from Kamada data by Tyler Busby, May 03 2024