A272402 Numbers k such that (26*10^k - 131)/3 is prime.

1, 2, 3, 5, 7, 10, 15, 20, 31, 107, 115, 290, 455, 611, 669, 1190, 2111, 2147, 2821, 4094, 4616, 7087, 7971, 11416, 12413, 21475, 23719, 24435, 32218, 122625, 160166, 190789

Offset: 1

Author

Robert Price, Apr 28 2016

Keywords

• nonn
• more

Comments

For k > 1, numbers k such that the digit 8 followed by k-2 occurrences of the digit 6 followed by the digits 23 is prime (see Example section).

a(33) > 2*10^5.

Examples

			3 is in this sequence because (26*10^3 - 131)/3 = 8623 is prime.
Initial terms and associated primes:
a(1) = 1, 43;
a(2) = 2, 823;
a(3) = 3, 8623;
a(4) = 5, 866623;
a(5) = 7, 86666623, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 86w23.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[(26*10^# - 131)/3] &]

PARI

isok(n) = isprime((26*10^n - 131)/3); \\ Michel Marcus, Apr 28 2016

Extensions

a(30)-a(32) from Robert Price, Oct 19 2019