A270738 Numbers k such that 23*10^k - 7 is prime.

1, 2, 3, 6, 8, 12, 18, 19, 30, 65, 77, 126, 353, 541, 576, 723, 777, 1024, 1194, 1507, 2379, 2615, 4008, 4295, 4495, 4526, 9996, 10348, 10673, 14120, 22350, 70240, 93116, 122070, 136225, 183710, 224232, 234025, 270799

Offset: 1

Author

Robert Price, Mar 22 2016

Keywords

• nonn
• more

Comments

Numbers k such that the digits 22 followed by k-1 occurrences of the digit 9 followed by the digit 3 is prime (see Example section).

a(40) > 3*10^5.

Examples

			3 is in this sequence because 23*10^3-7 = 22993 is prime.
Initial terms and associated primes:
a(1) = 1, 223;
a(2) = 2, 2293;
a(3) = 3, 22993;
a(4) = 6, 22999993;
a(5) = 8, 2299999993, etc.
		

Links

• Makoto Kamada, Search for 229w3.

Crossrefs

Cf. A056654, A268448, A269303, A270339, A270613.

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[23*10^# - 7] &] (* Corrected by Georg Fischer, Jul 22 2019 *)

PARI

lista(nn) = {for(n=1, nn, if(ispseudoprime(23*10^n - 7), print1(n, ", "))); } \\ Altug Alkan, Mar 22 2016

Extensions

a(34)-a(36) from Robert Price, Feb 25 2020

a(37)-a(39) from Robert Price, May 31 2023