A294391 Numbers k such that (68*10^k - 419)/9 is prime.

1, 2, 5, 8, 11, 13, 19, 23, 32, 55, 59, 173, 199, 386, 425, 494, 758, 2473, 4154, 15355, 47399, 122933

Offset

1,2

Comments

For k > 1, numbers k such that the digit 7 followed by k-2 occurrences of the digit 5 followed by the digits 09 is prime (see Example section).

a(23) > 2*10^5.

Links

Table of n, a(n) for n=1..22.

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

Makoto Kamada, Search for 75w09.

Example

2 is in this sequence because (68*10^2 - 419)/9 = 709 is prime.
Initial terms and associated primes:
a(1) = 1, 29;
a(2) = 2, 709;
a(3) = 5, 755509;
a(4) = 8, 755555509;
a(5) = 11, 755555555509; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[(68*10^# - 419)/9] &]

Prog

(PARI) isok(k) = isprime((68*10^k - 419)/9); \\ Michel Marcus, Oct 30 2017

Crossrefs

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

Sequence in context: A141207 A190057 A190305 * A257771 A276881 A282457

Adjacent sequences: A294388 A294389 A294390 * A294392 A294393 A294394

Keyword

nonn,more,hard

Author

Robert Price, Oct 29 2017

Extensions

a(22) from Robert Price, Jul 27 2019

Status

approved