A295624 Numbers k such that (38*10^k + 403)/9 is prime.

2, 5, 8, 11, 15, 17, 87, 146, 201, 287, 383, 489, 527, 4077, 5102, 7769, 22715, 25077, 37425, 82161, 180296

Offset

1,1

Comments

For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 2 followed by the digits 67 is prime (see Example section).

a(22) > 2*10^5.

Links

Table of n, a(n) for n=1..21.

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

Makoto Kamada, Search for 42w67.

Example

2 is in this sequence because (38*10^82 2 161+403)/9 = 467 is prime.
Initial terms and associated primes:
a(1) = 2, 467;
a(2) = 5, 422267;
a(3) = 8, 422222267;
a(4) = 11, 422222222267;
a(5) = 15, 4222222222222267; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(38*10^# + 403)/9] &]

Crossrefs

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

Sequence in context: A190079 A184872 A163249 * A284882 A190364 A088366

Adjacent sequences: A295621 A295622 A295623 * A295625 A295626 A295627

Keyword

nonn,more,hard

Author

Robert Price, Nov 24 2017

Extensions

a(21) from Robert Price, Oct 03 2018

Status

approved