A280205 Numbers k such that (16*10^k + 197) / 3 is prime.

0, 2, 3, 5, 8, 10, 111, 114, 456, 1158, 1241, 1462, 1736, 1827, 2523, 2812, 3305, 5392, 5897, 6174, 13683, 17088, 23771, 28448, 127259, 142058, 164122

Offset

1,2

Comments

For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 3 followed by the digits 99 is prime (see Example section).

a(28) > 2*10^5.

Links

Table of n, a(n) for n=1..27.

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

Makoto Kamada, Search for 53w99.

Example

3 is in this sequence because (16*10^3 + 197) / 3 = 5399 is prime.
Initial terms and associated primes:
a(1) = 0, 71;
a(2) = 2, 599;
a(3) = 3, 5399;
a(4) = 5, 533399;
a(5) = 8, 533333399; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(16*10^# + 197) / 3] &]

Prog

(PARI) is(n)=ispseudoprime((16*10^n + 197)/3) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

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

Sequence in context: A309527 A023176 A063178 * A276731 A028891 A028890

Adjacent sequences: A280202 A280203 A280204 * A280206 A280207 A280208

Keyword

nonn,more,hard

Author

Robert Price, Dec 28 2016

Extensions

a(25)-a(27) from Robert Price, Apr 03 2019

Status

approved