A294229 Numbers k such that (52*10^k + 119)/9 is prime.

0, 1, 3, 4, 9, 12, 13, 15, 30, 37, 58, 67, 142, 355, 442, 660, 1078, 3337, 5923, 10204, 21645, 50149

Offset

1,3

Comments

For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 7 followed by the digits 91 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 57w91.

Example

3 is in this sequence because (52*10^3 + 119)/9 = 5791 is prime.
Initial terms and associated primes:
a(1) = 0, 19;
a(2) = 1, 71;
a(3) = 3, 5791;
a(4) = 4, 57791;
a(5) = 9, 5777777791; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(52*10^# + 119)/9] &]

Crossrefs

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

Sequence in context: A327060 A270817 A182828 * A035256 A287400 A309758

Adjacent sequences: A294226 A294227 A294228 * A294230 A294231 A294232

Keyword

nonn,more,hard

Author

Robert Price, Oct 25 2017

Status

approved