A290962 Numbers k such that (13*10^k - 43)/3 is prime.

1, 2, 4, 5, 8, 12, 55, 125, 136, 221, 224, 668, 1254, 2639, 4745, 5888, 8526, 9139, 13771, 17936, 27713, 38668, 44680, 73891, 135184, 200610, 215592, 247793, 258710, 291721

Offset: 1

Author

Robert Price, Aug 15 2017

Keywords

• nonn
• more
• hard

Comments

For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 3 followed by the digits 19 is prime (see Example section).

a(31) > 3*10^5.

Examples

			2 is in this sequence because (13*10^2 - 43)/3 = 419 is prime.
Initial terms and associated primes:
a(1) = 1, 29;
a(2) = 2, 419;
a(3) = 4, 43319;
a(4) = 5; 433319;
a(5) = 8, 433333319; etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 43w19.

Crossrefs

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

Programs

Mathematica

Select[Range[1, 100000], PrimeQ[(13*10^# - 43)/3] &]

PARI

isok(n) = ispseudoprime((13*10^n - 43)/3) \\ Altug Alkan, Aug 15 2017

Extensions

a(25) from Robert Price, Nov 28 2018

a(26)-a(30) from Robert Price, Oct 26 2023