A293853 Numbers k such that (10^k - 79)/3 is prime.

2, 3, 4, 7, 9, 15, 57, 63, 147, 178, 202, 697, 713, 952, 1861, 7433, 14311, 16737, 29369, 72723, 121543

Offset

1,1

Comments

For k > 1, numbers k such that k-2 occurrences of the digit 3 followed by the digits 07 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 3w07.

Example

3 is in this sequence because (10^3 - 79)/3 = 307 is prime.
Initial terms and associated primes:
a(1) = 2, 7;
a(2) = 3, 307;
a(3) = 4, 3307;
a(4) = 7, 3333307;
a(5) = 9, 333333307; etc.

Mathematica

Select[Range[2, 100000], PrimeQ[(10^# - 79)/3] &]

Crossrefs

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

Sequence in context: A303665 A027947 A324736 * A067236 A320357 A250255

Adjacent sequences: A293850 A293851 A293852 * A293854 A293855 A293856

Keyword

nonn,more,hard

Author

Robert Price, Oct 17 2017

Extensions

a(21) from Robert Price, Jan 09 2018

Status

approved