A296052 Numbers k such that (41*10^k - 329)/9 is prime.

2, 3, 9, 18, 21, 99, 311, 437, 687, 761, 1451, 2088, 2559, 2898, 4974, 5058, 5798, 6776

Offset

1,1

Comments

For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 5 followed by the digits 19 is prime (see Example section).

a(19) > 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 45w19.

Example

2 is in this sequence because (41*10^2 - 329)/9 = 419 is prime.
Initial terms and associated primes:
a(1) = 2, 419;
a(2) = 3, 4519;
a(3) = 9, 4555555519;
a(4) = 18, 4555555555555555519;
a(5) = 21, 4555555555555555555519; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[(41*10^# - 329)/9] &]

Crossrefs

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

Sequence in context: A034467 A234646 A065965 * A108827 A298347 A113201

Adjacent sequences: A296049 A296050 A296051 * A296053 A296054 A296055

Keyword

nonn,more,hard

Author

Robert Price, Dec 03 2017

Status

approved