A257027 Numbers k such that 7*R_(k+2) - 6*10^k is prime, where R_k = 11...1 is the repunit (A002275) of length k.

0, 2, 3, 9, 11, 18, 74, 131, 144, 161, 224, 282, 390, 398, 614, 791, 1313, 1866, 9708, 10544, 13292, 13394, 29703, 30779, 72446

Offset

1,2

Comments

Also, numbers k such that (646*10^k - 7)/9 is prime.

Terms from Kamada.

a(26) > 10^5. Robert Price, Jul 31 2016

Links

Table of n, a(n) for n=1..25.

Makoto Kamada, Factorization of near-repdigit-related numbers.

Makoto Kamada, Search for 717w.

Index entries for primes involving repunits.

Example

For k=2, 7*R_4 - 6*10^2 = 7777 - 600 = 7177 which is prime.
a(1)=0 associated with 71, a(2)=2 associated with 7177, a(3)=3 associated with 71777, a(4)=9 associated with 71777777777, etc. - Robert Price, Jul 31 2016

Mathematica

Select[Range[0, 100000], PrimeQ[(646*10^#-7)/9 ] &]

Prog

(PARI) for(n=0, 200, if(isprime((646*10^n-7)/9), print1(n, ", "))) \\ Derek Orr, Apr 14 2015
(Magma) [n: n in [0..300] | IsPrime((646*10^n-7) div 9)]; // Vincenzo Librandi, Apr 15 2015

Crossrefs

Cf. A002275, A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

Sequence in context: A074338 A111319 A109658 * A271548 A369338 A110350

Adjacent sequences: A257024 A257025 A257026 * A257028 A257029 A257030

Keyword

more,hard,nonn

Author

Robert Price, Apr 14 2015

Extensions

a(25) from Robert Price, Jul 31 2016

Status

approved