A293396 Numbers k such that (13*10^k + 347)/9 is prime.

1, 3, 6, 9, 12, 18, 24, 31, 36, 39, 57, 91, 129, 529, 798, 1279, 1728, 6603, 12883, 29463, 77811

Offset

1,2

Comments

For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 4 followed by the digits 83 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 14w83.

Example

3 is in this sequence because (13*10^3 + 347)/9 = 1483 is prime.
Initial terms and associated primes:
a(1) = 1, 53;
a(2) = 3, 1483;
a(3) = 6, 1444483;
a(4) = 9, 1444444483;
a(5) = 12, 1444444444483; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(13*10^# + 347)/9] &]

Prog

(PARI) isok(k) = isprime((13*10^k + 347)/9); \\ Altug Alkan, Oct 08 2017

Crossrefs

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

Sequence in context: A156997 A063996 A065119 * A173195 A354785 A232920

Adjacent sequences: A293393 A293394 A293395 * A293397 A293398 A293399

Keyword

nonn,more,hard

Author

Robert Price, Oct 08 2017

Status

approved