A286092 Numbers k such that (199*10^k + 11)/3 is prime.

2, 3, 8, 10, 13, 19, 20, 26, 37, 39, 232, 308, 381, 382, 706, 872, 1707, 1929, 2195, 9211, 15567, 58306

Offset

1,1

Comments

For k > 0, numbers k such that the digits 66 followed by k-1 occurrences of the digit 3 followed by the digit 7 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 663w7.

Example

3 is in this sequence because (199*10^3 + 11)/3 = 66337 is prime.
Initial terms and associated primes:
a(1) = 2, 6637;
a(2) = 3, 66337;
a(3) = 8, 6633333337;
a(4) = 10, 663333333337;
a(5) = 13, 663333333333337; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(199*10^# + 11)/3] &]

Crossrefs

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

Sequence in context: A360940 A132327 A281929 * A100317 A376266 A295030

Adjacent sequences: A286089 A286090 A286091 * A286093 A286094 A286095

Keyword

nonn,more,hard

Author

Robert Price, May 01 2017

Status

approved