A282340 Numbers k such that (184*10^k - 1)/3 is prime.

0, 1, 2, 3, 21, 24, 25, 39, 42, 90, 192, 547, 3185, 3363, 4279, 4496, 4761, 5022, 6807, 13220, 13283, 13519, 25183, 37609, 84348, 87473, 112007, 211682

Offset

1,3

Comments

Numbers k such that the digits 61 followed by k occurrences of the digit 3 is prime (see Example section).

a(29) > 3*10^5.

Links

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

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

Makoto Kamada, Search for 613w.

Example

2 is in this sequence because (184*10^2 - 1)/3 = 6133 is prime.
Initial terms and associated primes:
a(1) = 0, 61;
a(2) = 1, 613;
a(3) = 2, 6133;
a(4) = 3, 61333;
a(5) = 21, 61333333333333333333333; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(184*10^# - 1)/3] &]

Prog

(PARI) isok(k) = isprime((184*10^k - 1)/3); \\ Michel Marcus, Feb 12 2017

Crossrefs

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

Sequence in context: A124447 A250181 A024765 * A248953 A090122 A328734

Adjacent sequences: A282337 A282338 A282339 * A282341 A282342 A282343

Keyword

nonn,more,hard

Author

Robert Price, Feb 12 2017

Extensions

a(27) from Robert Price, Feb 26 2020

a(28) from Robert Price, Jul 02 2023

Status

approved