A282277 Numbers k such that (23*10^k + 97)/3 is prime.

3, 6, 11, 14, 20, 38, 55, 206, 1327, 1676, 1715, 1814, 2030, 2406, 2599, 3251, 4493, 5066, 6029, 8745, 24918, 26672, 70363, 77556

Offset

1,1

Comments

For k > 1, numbers k such that the digit 7 followed by k-2 occurrences of the digit 6 followed by the digits 99 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 76w99.

Example

6 is in this sequence because (23*10^6 + 97)/3 = 7666699 is prime.
Initial terms and associated primes:
a(1) = 3, 7699;
a(2) = 6, 7666699;
a(3) = 11, 766666666699;
a(4) = 14, 766666666666699;
a(5) = 20, 766666666666666666699; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(23*10^# + 97)/3] &]

Crossrefs

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

Sequence in context: A267519 A200182 A342173 * A122599 A342954 A015823

Adjacent sequences: A282274 A282275 A282276 * A282278 A282279 A282280

Keyword

nonn,more,hard

Author

Robert Price, Feb 10 2017

Status

approved