A280584 Numbers k such that (14*10^k - 83)/3 is prime.

1, 2, 3, 4, 6, 10, 11, 24, 53, 83, 97, 156, 157, 162, 182, 233, 355, 499, 629, 1252, 6378, 8366, 26406, 35345, 107694, 126784, 195234, 255805

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 39 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 46w39.

Example

4 is in this sequence because (14*10^4 - 83) / 3 = 46639 is prime.
Initial terms and associated primes:
a(1) = 1, 19;
a(2) = 2, 439;
a(3) = 3, 4639;
a(4) = 4, 46639;
a(5) = 6, 4666639; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[(14*10^# - 83) / 3] &]

Prog

(PARI) is(n)=ispseudoprime((14*10^n - 83)/3) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

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

Sequence in context: A005453 A180242 A187966 * A225649 A225651 A191149

Adjacent sequences: A280581 A280582 A280583 * A280585 A280586 A280587

Keyword

nonn,more,hard

Author

Robert Price, Jan 05 2017

Extensions

a(25)-a(27) from Robert Price, Dec 23 2018

a(28) from Robert Price, Jun 17 2023

Status

approved