A281169 Numbers k such that (58*10^k - 1)/3 is prime.

0, 1, 2, 3, 25, 66, 123, 129, 146, 371, 834, 929, 1361, 1568, 2065, 2220, 3482, 3693, 4776, 13742, 15686, 16473, 21566, 38400

Offset

1,3

Comments

Numbers k such that the digits 19 followed by k occurrences of the digit 3 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 193w.

Example

2 is in this sequence because (58*10^2 - 1) / 3 = 1933 is prime.
Initial terms and associated primes:
a(1) = 0, 19;
a(2) = 1, 193;
a(3) = 2, 1933;
a(4) = 3, 19333;
a(5) = 25, 193333333333333333333333333; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(58*10^# - 1) / 3] &]

Crossrefs

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

Sequence in context: A320223 A296275 A295328 * A296281 A226018 A094998

Adjacent sequences: A281166 A281167 A281168 * A281170 A281171 A281172

Keyword

nonn,more,hard

Author

Robert Price, Jan 16 2017

Status

approved