A293687 Numbers k such that (11*10^k - 137)/9 is prime.

2, 5, 21, 23, 47, 75, 107, 110, 188, 261, 617, 872, 965, 2735, 10145, 12572, 13364, 14570, 195350

Offset

1,1

Comments

For k > 1, numbers such that the digit 1 followed by k-2 occurrences of the digit 2 followed by the digits 07 is prime (see Example section).

a(20) > 2*10^5.

Links

Table of n, a(n) for n=1..19.

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

Makoto Kamada, Search for 12w07

Example

2 is in this sequence because (11*10^2 - 137)/9 = 107 is prime.
Initial terms and primes associated:
a(1) = 2, 107;
a(2) = 5, 122207;
a(3) = 21, 1222222222222222222207;
a(4) = 23, 122222222222222222222207;
a(5) = 47, 122222222222222222222222222222222222222222222207; etc.

Mathematica

Select[Range[2, 100000], PrimeQ[(11*10^# - 137)/9] &]

Prog

(PARI) isok(k) = isprime((11*10^k - 137)/9); \\ Michel Marcus, Nov 15 2017

Crossrefs

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

Sequence in context: A088498 A240147 A358556 * A190117 A230656 A266950

Adjacent sequences: A293684 A293685 A293686 * A293688 A293689 A293690

Keyword

nonn,more,hard

Author

Robert Price, Nov 15 2017

Extensions

a(19) from Robert Price, Jan 26 2018

Status

approved