A273944 Numbers k such that (266*10^k - 17)/3 is prime.

0, 1, 2, 3, 7, 8, 11, 14, 24, 29, 50, 78, 99, 192, 226, 519, 613, 651, 1492, 3720, 6567, 6791, 7226, 8471, 9050, 13521, 14255, 33529, 44072, 47844, 64102, 112930, 116024, 122872, 138328, 140681, 268407

Offset: 1

Author

Robert Price, Jun 17 2016

Keywords

• nonn
• more

Comments

For k > 1, numbers k such that the digits 88 followed by k-1 occurrences of the digit 6 followed by the digit 1 is prime (see Example section).

a(38) > 3*10^5.

Examples

			3 is in this sequence because (266*10^3-17)/3 = 88661 is prime.
Initial terms and associated primes:
a(1) = 0, 83;
a(2) = 1, 881;
a(3) = 2, 8861;
a(4) = 3, 88661;
a(5) = 7, 886666661, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 886w1.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[(266*10^# - 17)/3] &]

PARI

isok(n) = isprime((266*10^n - 17)/3); \\ Michel Marcus, Jun 18 2016

Extensions

a(32)-a(36) from Robert Price, Jul 16 2020

a(37) from Robert Price, Jun 21 2023