A282351 Numbers k such that (13*10^k + 437)/9 is prime.

2, 3, 6, 14, 17, 29, 41, 44, 87, 213, 354, 840, 972, 1263, 2018, 2534, 4868, 7992, 13676, 18354, 19304, 40515, 126638, 135279

Offset

1,1

Comments

For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 4 followed by the digits 93 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 14w93.

Example

3 is in this sequence because (13*10^3 + 437)/9 = 1493 is prime.
Initial terms and associated primes:
a(1) = 2, 193;
a(2) = 3, 1493;
a(3) = 6, 1444493;
a(4) = 14, 144444444444493;
a(5) = 17, 144444444444444493; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(13*10^# + 437)/9] &]

Crossrefs

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

Sequence in context: A078557 A005537 A306600 * A193093 A182756 A152092

Adjacent sequences: A282348 A282349 A282350 * A282352 A282353 A282354

Keyword

nonn,more,hard

Author

Robert Price, Feb 12 2017

Extensions

a(23)-a(24) from Robert Price, Apr 14 2018

Status

approved