A275067 Numbers k such that 7*10^k + 39 is prime.

1, 2, 3, 4, 12, 19, 26, 32, 84, 164, 199, 251, 306, 510, 641, 1028, 1147, 1802, 1948, 2058, 2243, 2257, 4282, 7900, 7941, 10179, 10723, 13570, 20565, 29132, 34947, 63493, 87319, 107870, 183511, 183596, 209161, 227178, 273983, 287854

Offset: 1

Author

Robert Price, Jul 15 2016

Keywords

• nonn
• more

Comments

For k > 1, numbers k such that the digit 7 followed by k-2 occurrences of the digit 0 followed by the digits 39 is prime (see Example section).

a(41) > 3*10^5.

Examples

			3 is in this sequence because 7*10^3 + 39 = 7039 is prime.
Initial terms and associated primes:
a(1) = 1, 109;
a(2) = 2, 739;
a(3) = 3, 7039;
a(4) = 4, 70000039;
a(5) = 12, 7000000000039, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 70w39.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[7*10^# + 39] &]

PARI

is(n)=ispseudoprime(7*10^n+39) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(34)-a(40) from Robert Price, Jul 02 2023