A269303 Numbers k such that (266*10^k + 1)/3 is prime.

0, 1, 2, 3, 4, 5, 6, 8, 10, 13, 19, 26, 37, 69, 77, 81, 214, 242, 255, 900, 1113, 1833, 3166, 3566, 4753, 4849, 4869, 5005, 7372, 7702, 10240, 16100, 18972, 28574, 33815, 37820, 70457, 89482, 106066, 133603, 154897, 278325

Offset: 1

Author

Robert Price, Feb 22 2016

Keywords

• nonn
• more

Comments

For k > 0, numbers k such that digits 88 followed by k-1 occurrences of digit 6 followed by the digit 7 is prime (see Example section).

a(43) > 3*10^5.

Examples

			6 is in this sequence because (266*10^n+1)/3 = 88666667 is prime.
Initial terms and associated primes:
a(1)  = 0,    89;
a(2)  = 1,    887;
a(3)  = 2,    8867;
a(4)  = 3,    88667;
a(5)  = 4,    886667;
a(6)  = 5,    8866667;
a(7)  = 6,    88666667;
a(8)  = 8,    8866666667;
a(9)  = 10,   886666666667;
a(10) = 13,   886666666666667, etc.
		

Links

• Makoto Kamada, Search for 886w7.

Crossrefs

Cf. A056654, A268448.

Programs

Magma

[n: n in [0..220] | IsPrime((266*10^n + 1) div 3)]; // Vincenzo Librandi, Feb 23 2016

Mathematica

Select[Range[0, 100000], PrimeQ[(266*10^#+1)/3] &]

PARI

is(n)=ispseudoprime((266*10^n + 1)/3) \\ Charles R Greathouse IV, Feb 16 2017

Extensions

a(39)-a(41) from Robert Price, Apr 22 2020

a(42) from Robert Price, May 31 2023