A272717 Numbers k such that (65*10^k + 691)/9 is prime.

1, 5, 7, 17, 35, 46, 56, 148, 187, 190, 256, 551, 553, 1033, 1751, 1976, 2696, 3116, 3364, 5353, 5893, 8063, 9548, 10640, 24655, 77992

Offset: 1

Author

Robert Price, Aug 11 2016

Keywords

• nonn
• more

Comments

For k > 1, numbers k such that the digit 7 followed by k-2 occurrences of the digit 2 followed by the digits 99 is prime (see Example section).

a(27) > 10^5.

Examples

			5 is in this sequence because (65*10^5+691)/9 = 722299 is prime.
Initial terms and associated primes:
a(1) = 1, 149;
a(2) = 5, 722299;
a(3) = 7, 72222299;
a(4) = 17, 722222222222222299;
a(5) = 35, 722222222222222222222222222222222299, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 72w99.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[(65*10^#+691)/9] &]

PARI

is(n)=ispseudoprime((65*10^n+691)/9) \\ Charles R Greathouse IV, Jun 13 2017