A293684 Numbers k such that (19*10^k + 413)/9 is prime.

1, 2, 4, 7, 11, 22, 28, 29, 38, 62, 316, 989, 1532, 2068, 2495, 3431, 4775, 9082, 14935, 15572, 39511, 43283, 66748

Offset

1,2

Comments

For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 2 followed by the digits 57 is prime (see Example section).

a(24) > 2*10^5.

Links

Table of n, a(n) for n=1..23.

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

Makoto Kamada, Search for 21w57.

Example

2 is in this sequence because (19*10^2 + 413)/9 = 257 is prime.
Initial terms and associated primes:
a(1) = 1, 67;
a(2) = 2, 257;
a(3) = 4, 21157;
a(4) = 7, 21111157;
a(5) = 11, 211111111157; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(19*10^# + 413)/9] &]

Crossrefs

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

Sequence in context: A024927 A018077 A114347 * A332274 A071250 A084992

Adjacent sequences: A293681 A293682 A293683 * A293685 A293686 A293687

Keyword

nonn,more,hard

Author

Robert Price, Oct 14 2017

Status

approved