A272999 Numbers k such that (11*10^k + 49)/3 is prime.

1, 2, 4, 5, 7, 10, 11, 16, 18, 21, 22, 30, 41, 69, 83, 128, 166, 190, 262, 263, 353, 496, 1398, 1793, 2806, 9722, 15733, 32420, 61095, 77909, 110496

Offset: 1

Author

Robert Price, May 12 2016

Keywords

• nonn
• more

Comments

For k > 1, numbers k such that the digit 3 followed by k-2 occurrences of the digit 6 followed by the digits 83 is prime (see Example section).

a(32) > 3*10^5.

Examples

			4 is in this sequence because (11*10^4 + 49)/3 = 36683 is prime.
Initial terms and associated primes:
a(1) = 1, 53;
a(2) = 2, 383:
a(3) = 4, 36683;
a(4) = 5, 366683;
a(5) = 7, 36666683, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 36w83.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[(11*10^# + 49)/3] &]

PARI

is(n)=ispseudoprime((11*10^n + 49)/3) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(31) from Robert Price, Jul 19 2018