A274336 Numbers k such that (16*10^k - 91)/3 is prime.

1, 2, 3, 5, 16, 18, 22, 31, 40, 98, 99, 192, 233, 367, 501, 1102, 1381, 1416, 2018, 6156, 6860, 7377, 14004, 16634, 21422, 27654, 85473, 260256, 265052, 274251

Offset: 1

Author

Robert Price, Jun 22 2016

Keywords

• nonn
• more

Comments

For k > 1, numbers k such that the digit 5 followed by k-1 occurrences of the digit 3 followed by the digits 03 is prime (see Example section).

a(31) > 3*10^5.

Examples

			3 is in this sequence because (16*10^3 - 91)/3 = 5303 is prime.
Initial terms and associated primes:
a(1) = 1, 23;
a(2) = 2, 503;
a(3) = 3, 5303;
a(4) = 5, 533303;
a(5) = 16, 53333333333333303, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 53w03.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[(16*10^# - 91)/3] &]

PARI

is(n)=ispseudoprime((16*10^n - 91)/3) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(28)-a(30) from Robert Price, Jun 01 2023