A283447 Numbers k such that (4*10^k + 197)/3 is prime.

0, 1, 2, 3, 4, 9, 12, 36, 42, 46, 75, 97, 153, 174, 204, 1078, 1306, 1380, 2096, 2401, 3393, 9547, 16650, 41404, 64014

Offset

1,3

Comments

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

a(26) > 2*10^5.

Links

Table of n, a(n) for n=1..25.

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

Makoto Kamada, Search for 13w99.

Example

3 is in this sequence because (4*10^3 + 197)/3 = 1399 is prime.
Initial terms and associated primes:
a(1) = 0, 67;
a(2) = 1, 79;
a(3) = 2, 199;
a(4) = 3, 1399;
a(5) = 4, 13399; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(4*10^# + 197)/3] &]

Prog

(PARI) isok(n) = isprime((4*10^n + 197)/3); \\ Indranil Ghosh, Mar 09 2017

Crossrefs

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

Sequence in context: A283596 A281992 A100902 * A034793 A134313 A307403

Adjacent sequences: A283444 A283445 A283446 * A283448 A283449 A283450

Keyword

nonn,more,hard

Author

Robert Price, Mar 07 2017

Status

approved