A271646 Numbers k such that 22*10^k + 7 is prime.

0, 1, 2, 9, 13, 14, 15, 17, 22, 23, 80, 297, 393, 524, 591, 1107, 1135, 1179, 1442, 2819, 3549, 3756, 3837, 4903, 5277, 5639, 7230, 13147, 14828, 16158, 18119, 28880, 99275, 212339, 254639

Offset: 1

Author

Robert Price, Apr 11 2016

Keywords

• nonn
• more

Comments

For k > 1, numbers k such that the digits 22 followed by k-1 occurrences of the digit 0 followed by the digit 7 is prime (see Example section).

a(36) > 3*10^5.

Examples

			2 is in this sequence because 22*10^2+7 = 227 is prime.
Initial terms and associated primes:
a(1) = 0, 29;
a(2) = 1, 227;
a(3) = 2, 2207;
a(4) = 9, 22000000007;
a(5) = 13, 220000000000007, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 220w7.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[22*10^# + 7] &]

PARI

is(n)=ispseudoprime(22*10^n + 7) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(34)-a(35) from Robert Price, Jun 01 2023