A272929 Numbers k such that (8*10^k - 77)/3 is prime.

2, 4, 5, 6, 15, 18, 43, 45, 55, 60, 105, 128, 180, 207, 271, 479, 869, 1220, 1478, 1937, 4003, 4213, 5503, 9562, 11388, 13120, 34049, 47178, 156371, 271039

Offset: 1

Author

Robert Price, May 10 2016

Keywords

• nonn
• more

Comments

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

a(31) > 3*10^5.

Examples

			4 is in this sequence because (8*10^4 - 77)/3 = 26641 is prime.
Initial terms and associated primes:
a(1) = 2, 241;
a(2) = 4, 26641;
a(3) = 5, 266641;
a(4) = 6, 2666641;
a(5) = 15, 2666666666666641, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 26w41.

Crossrefs

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

Programs

Mathematica

Select[Range[1, 100000], PrimeQ[(8*10^# - 77)/3] &]

PARI

lista(nn) = {for(n=1, nn, if(ispseudoprime((8*10^n - 77)/3), print1(n, ", ")));} \\ Altug Alkan, May 11 2016

Extensions

a(29) from Robert Price, Jul 07 2018

a(30) from Robert Price, Jul 02 2023