A293758 Numbers k such that (7*10^k + 167)/3 is prime.

1, 3, 6, 7, 8, 12, 37, 44, 68, 111, 126, 142, 376, 409, 8179, 8566, 9208, 9406, 14841, 26128, 52819, 61696, 89383

Offset

1,2

Comments

For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 3 followed by the digits 89 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 23w89.

Example

3 is in this sequence because (7*10^3 + 167)/3 = 2389 is prime.
Initial terms and associated primes:
a(1) = 1, 79;
a(2) = 3, 2389;
a(3) = 6, 2333389;
a(4) = 7, 23333389;
a(5) = 8, 233333389; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(7*10^# + 167)/3] &]

Crossrefs

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

Sequence in context: A310132 A189659 A157041 * A222305 A189098 A241007

Adjacent sequences: A293755 A293756 A293757 * A293759 A293760 A293761

Keyword

nonn,more,hard

Author

Robert Price, Oct 15 2017

Status

approved