A280558 Numbers k such that (13*10^k + 89) / 3 is prime.

1, 2, 3, 6, 10, 12, 18, 34, 42, 61, 76, 85, 94, 178, 348, 451, 1123, 1455, 2234, 4519, 7502, 16036, 24216, 156522

Offset

1,2

Comments

For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 3 followed by the digits 63 is prime (see Example section).

a(25) > 2*10^5.

Links

Table of n, a(n) for n=1..24.

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

Makoto Kamada, Search for 43w63.

Example

3 is in this sequence because (13*10^3 + 89) / 3 = 4363 is prime.
Initial terms and associated primes:
a(1) = 1, 73;
a(2) = 2, 463;
a(3) = 3, 4363;
a(4) = 6, 4333363;
a(5) = 10, 43333333363; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(13*10^# + 89) / 3] &]

Prog

(PARI) is(n)=ispseudoprime((13*10^n + 89)/3) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

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

Sequence in context: A038775 A065029 A239212 * A216920 A120754 A023547

Adjacent sequences: A280555 A280556 A280557 * A280559 A280560 A280561

Keyword

nonn,more,hard

Author

Robert Price, Jan 05 2017

Extensions

a(24) from Robert Price, Sep 10 2018

Status

approved