A291178 Numbers k such that (13*10^k - 37)/3 is prime.

1, 2, 4, 7, 8, 26, 64, 116, 123, 157, 178, 288, 328, 1730, 2712, 3244, 3865, 7766, 8792, 9512, 14917, 33912, 39058, 57997, 120306, 150675, 171306, 173467, 175965

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 21 is prime (see Example section).

a(30) > 2*10^5.

Links

Table of n, a(n) for n=1..29.

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

Makoto Kamada, Search for 43w21.

Example

4 is in this sequence because (13*10^4 - 37)/3 = 43321 is prime.
Initial terms and associated primes:
a(1) = 1, 31;
a(2) = 2, 421;
a(3) = 4, 43321;
a(4) = 7, 43333321;
a(5) = 8, 433333321; etc.

Mathematica

Select[Range[2, 100000], PrimeQ[(13*10^# - 37)/3] &]

Prog

(PARI) isok(n) = isprime((13*10^n - 37)/3); \\ Altug Alkan, Aug 21 2017

Crossrefs

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

Sequence in context: A122979 A122980 A012985 * A023145 A094446 A370003

Adjacent sequences: A291175 A291176 A291177 * A291179 A291180 A291181

Keyword

nonn,more,hard

Author

Robert Price, Aug 19 2017

Extensions

a(25)-a(29) from Robert Price, Jan 01 2019

Status

approved