A276353 Numbers k such that (19*10^k + 77) / 3 is prime.

1, 2, 3, 5, 6, 17, 22, 56, 71, 90, 93, 109, 124, 135, 179, 255, 1804, 2541, 2707, 3195, 4952, 5884, 9301, 19847, 27903, 45739, 65545, 69424, 103907, 160619, 168173, 297497, 299640

Offset: 1

Author

Robert Price, Aug 31 2016

Keywords

• nonn
• more

Comments

For k > 1, numbers k such that the digit 6 followed by k-2 occurrences of the digit 3 followed by the digits 59 is prime (see Example section).

a(34) > 3*10^5.

Examples

			3 is in this sequence because (19*10^3 + 77) / 3 = 6359 is prime.
Initial terms and associated primes:
a(1) = 1, 89;
a(2) = 2, 659
a(3) = 3, 6359;
a(4) = 5, 633359;
a(5) = 6, 6333359, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 63w59.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[(19*10^# + 77) / 3] &]

PARI

is(n)=ispseudoprime((19*10^n + 77)/3) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(29)-a(31) from Robert Price, May 28 2019

a(32)-a(33) from Robert Price, Jun 01 2023