A257025 Numbers k such that 3*R_(k+2) + 4*10^k is prime, where R_k = 11...1 is the repunit (A002275) of length k.

0, 1, 2, 5, 7, 14, 32, 65, 163, 398, 485, 1799, 1852, 3326, 3692, 7226, 12743, 15313, 110405, 120395, 132337, 140357, 153025, 194150

Offset

1,3

Comments

Also, numbers k such that (112*10^k - 1)/3 is prime.

Terms from Kamada.

a(25) > 250000.

Links

Table of n, a(n) for n=1..24.

Makoto Kamada, Near-repdigit numbers of the form ABAA...AA.

Makoto Kamada, Prime numbers of the form 3733...33.

Index entries for primes involving repunits.

Example

For k=2, 3*R_4 + 4*10^2 = 3333 + 400 = 3733 which is prime.

Mathematica

Select[Range[0, 250000], PrimeQ[(112*10^#-1)/3 ] &]

Prog

(PARI) for(n=0, 500, if(isprime((112*10^n-1)/3), print1(n, ", "))) \\ Derek Orr, Apr 14 2015
(Magma) [n: n in [0..300] | IsPrime((112*10^n-1) div 3)]; // Vincenzo Librandi, Apr 15 2015

Crossrefs

Cf. A002275.

Sequence in context: A338231 A286573 A133511 * A076720 A245921 A215513

Adjacent sequences: A257022 A257023 A257024 * A257026 A257027 A257028

Keyword

more,hard,nonn

Author

Robert Price, Apr 14 2015

Status

approved