A276698 Numbers k such that (25*10^k - 37) / 3 is prime.

1, 2, 7, 17, 24, 32, 66, 67, 74, 92, 104, 117, 188, 260, 279, 336, 348, 369, 547, 619, 860, 2735, 7932, 11874, 14867, 40153, 171849, 176715

Offset: 1

Author

Robert Price, Sep 14 2016

Keywords

• nonn
• more

Comments

For k > 1, numbers k such that the digit 8 followed by k-2 occurrences of the digit 3 followed by the digits 21 is prime (see Example section).

a(29) > 2*10^5.

Examples

			2 is in this sequence because (25*10^2 - 37) / 3 = 821 is prime.
Initial terms and associated primes:
a(1) = 1, 71;
a(2) = 2, 821;
a(3) = 7, 83333321;
a(4) = 17, 833333333333333321;
a(5) = 24, 8333333333333333333333321, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 83w21.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[(25*10^# - 37) / 3] &]

PARI

is(n)=ispseudoprime((25*10^n - 37)/3) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(27)-a(28) from Robert Price, Oct 07 2019