A295033 Numbers k such that (5*10^k + 79)/3 is prime.

1, 2, 3, 4, 5, 8, 9, 20, 291, 417, 712, 749, 1906, 2086, 2746, 3896, 4927, 10058, 18369, 34071, 36569, 44749, 89510, 139457

Offset

1,2

Comments

For k > 1, numbers such that the digit 1 followed by k-2 occurrences of the digit 6 followed by the digits 93 is prime (see Example section).

a(25) > 2*10^5.

Links

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

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

Makoto Kamada, Search for 16w93

Example

2 is in this sequence because (5*10^2 + 79)/3 = 193 is prime.
Initial terms and primes associated:
a(1) = 1, 43;
a(2) = 2, 193;
a(3) = 3, 1693;
a(4) = 4, 16693;
a(5) = 5, 166693; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(5*10^# + 79)/3] &]

Prog

(PARI) is(k) = ispseudoprime((5*10^k + 79)/3) \\ Iain Fox, Nov 12 2017

Crossrefs

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

Sequence in context: A306044 A263581 A120430 * A152606 A057911 A085266

Adjacent sequences: A295030 A295031 A295032 * A295034 A295035 A295036

Keyword

nonn,more,hard

Author

Robert Price, Nov 12 2017

Extensions

a(24) from Robert Price, Mar 09 2018

Status

approved