A294915 Numbers k such that (13*10^k - 139)/9 is prime.

3, 7, 46, 51, 87, 124, 141, 301, 309, 400, 667, 1749, 2512, 3859, 4323, 4515, 9238, 9592

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 29 is prime (see Example section).

a(18) > 2*10^5.

Links

Table of n, a(n) for n=1..18.

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

Makoto Kamada, Search for 14w29.

Example

3 is in this sequence because (13*10^3 - 139)/9 = 1429 is prime.
Initial terms and associated primes:
a(1) = 3, 1429;
a(2) = 7, 14444429;
a(3) = 46, 14444444444444444444444444444444444444444444429;
a(4) = 51, 1444444444444444444444444444444444444444444444444429;  etc.

Mathematica

Select[Range[2, 100000], PrimeQ[(13*10^# - 139)/9] &]

Crossrefs

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

Sequence in context: A365572 A301324 A184339 * A003758 A231893 A132565

Adjacent sequences: A294912 A294913 A294914 * A294916 A294917 A294918

Keyword

nonn,more,hard

Author

Robert Price, Nov 10 2017

Status

approved