A271506 Numbers k such that (7*10^k + 179)/3 is prime.

1, 2, 3, 7, 8, 36, 41, 46, 74, 76, 88, 103, 115, 188, 194, 257, 310, 399, 511, 515, 776, 1134, 1404, 6545, 6569, 17600, 22209, 24397, 24842, 46957, 116684, 118607, 131339, 202267

Offset: 1

Author

Robert Price, Apr 08 2016

Keywords

• nonn
• more

Comments

For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 3 followed by the digits 93 is prime (see Example section).

a(35) > 3*10^5.

Examples

			3 is in this sequence because (7*10^3 + 179)/3 = 2393 is prime.
Initial terms and associated primes:
a(1) = 1, 83;
a(2) = 2, 293;
a(3) = 3, 2393;
a(4) = 7, 23333393;
a(5) = 8, 233333393. etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 23w93.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[(7*10^# + 179)/3] &]
Join[{1},Flatten[Position[Table[100*FromDigits[PadRight[{2},n,3]]+93,{n,47000}],?PrimeQ]]+1] (* _Harvey P. Dale, Dec 11 2018 *)

PARI

is(n)=ispseudoprime((7*10^n+179)/3) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(31)-a(33) from Robert Price, Sep 01 2018

a(34) from Robert Price, Jun 21 2023