A273371 Numbers k such that (17*10^k - 77)/3 is prime.

1, 2, 3, 6, 9, 15, 21, 26, 33, 42, 131, 168, 434, 464, 501, 1004, 1011, 1089, 1509, 2025, 2283, 2526, 9150, 9464, 14139, 14827, 18941, 32426, 36719, 42933, 138569

Offset: 1

Author

Robert Price, May 20 2016

Keywords

• nonn
• more

Comments

For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 6 followed by the digits 41 is prime (see Example section).

a(32) > 3*10^5.

Examples

			3 is in this sequence because (17*10^3-77)/3 = 5641 is prime.
Initial terms and associated primes:
a(1) = 1, 31;
a(2) = 2, 541;
a(3) = 3, 5641;
a(4) = 6, 5666641;
a(5) = 9, 5666666641, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 56w41.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[(17*10^# - 77)/3] &]

PARI

is(n)=ispseudoprime((17*10^n - 77)/3) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(31) from Robert Price, Aug 21 2019