A272193 Numbers k such that (73*10^k + 143)/9 is prime.

1, 2, 5, 7, 13, 16, 17, 25, 44, 52, 197, 233, 241, 389, 838, 856, 2252, 2945, 5207, 8020, 10708, 14663, 16885, 20366, 20450, 24121, 24437, 29348, 134939

Offset: 1

Author

Robert Price, Apr 22 2016

Keywords

• nonn
• more

Comments

For k > 1, numbers k such that the digit 8 followed by k-2 occurrences of the digit 1 followed by the digits 27 is prime (see Example section).

a(29) > 2*10^5.

Examples

			5 is in this sequence because (73*10^5 + 143)/9 = 811127 is prime.
Initial terms and associated primes:
a(1) = 1, 97;
a(2) = 2, 827;;
a(3) = 5, 811127;
a(4) = 7, 81111127;
a(5) = 13, 81111111111127, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 81w27.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[(73*10^# + 143)/9] &]

PARI

lista(nn) = for(n=1, nn, if(ispseudoprime((73*10^n + 143)/9), print1(n, ", "))); \\ Altug Alkan, Apr 22 2016

Extensions

a(29) from Robert Price, Jul 31 2019