A276546 Numbers k such that (151*10^k - 1)/3 is prime.

1, 3, 6, 15, 19, 34, 37, 88, 141, 216, 239, 246, 288, 365, 429, 762, 1879, 2309, 9555, 19843, 28348, 45058, 62879, 86963, 90669, 148020, 148601, 199003, 289877

Offset: 1

Author

Robert Price, Apr 09 2017

Keywords

• nonn
• more
• hard

Comments

Numbers k such that the digits 50 followed by k occurrences of the digit 3 is prime (see Example section).

a(30) > 3*10^5.

Examples

			3 is in this sequence because (151*10^3 - 1)/3 = 50333 is prime.
Initial terms and associated primes:
a(1) = 1, 503;
a(2) = 3, 50333;
a(3) = 6, 50333333;
a(4) = 15, 50333333333333333;
a(5) = 19, 503333333333333333333; etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 503w.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[(151*10^# - 1)/3] &]

Extensions

a(26)-a(28) from Robert Price, Mar 17 2020

a(29) from Robert Price, Oct 25 2023