A280206 Numbers k such that (14*10^k - 53) / 3 is prime.

1, 2, 3, 4, 5, 11, 28, 40, 65, 95, 187, 201, 202, 211, 316, 331, 559, 746, 1307, 2139, 3571, 5843, 6545, 12717, 32804, 46389, 72326, 135301

Offset

1,2

Comments

For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 6 followed by the digits 49 is prime (see Example section).

a(29) > 2*10^5.

Links

Table of n, a(n) for n=1..28.

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

Makoto Kamada, Search for 46w49.

Example

3 is in this sequence because (14*10^3 - 53) / 3 = 4649 is prime.
Initial terms and associated primes:
a(1) = 1, 29;
a(2) = 2, 449;
a(3) = 3, 4649;
a(4) = 4, 46649;
a(5) = 5, 466649; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[(14*10^# - 53) / 3] &]

Prog

(PARI) is(n)=ispseudoprime((14*10^n - 53)/3) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

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

Sequence in context: A064959 A217650 A032988 * A190783 A136367 A014545

Adjacent sequences: A280203 A280204 A280205 * A280207 A280208 A280209

Keyword

nonn,more,hard

Author

Robert Price, Dec 28 2016

Extensions

a(28) from Robert Price, Dec 17 2018

Status

approved