A293591 Numbers k such that (7*10^k + 113)/3 is prime.

1, 2, 3, 4, 5, 8, 18, 30, 95, 165, 805, 2738, 3038, 5953, 6009, 7205, 9631, 17495, 27745, 28449, 62278, 106516, 130825, 153664

Offset

1,2

Comments

For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 3 followed by the digits 71 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 23w71.

Example

2 is in this sequence because (7*10^2 + 113)/3 = 271 is prime.
Initial terms and associated primes:
a(1) = 1, 61;
a(2) = 2, 271;
a(3) = 3, 2371;
a(4) = 4, 23371;
a(5) = 5, 233371; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(7*10^# + 113)/3] &]

Crossrefs

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

Sequence in context: A055638 A375285 A057657 * A116657 A268274 A079383

Adjacent sequences: A293588 A293589 A293590 * A293592 A293593 A293594

Keyword

nonn,more,hard

Author

Robert Price, Oct 12 2017

Extensions

a(22)-a(24) from Robert Price, Feb 21 2018

Status

approved