A273006 Numbers k such that 88*10^k + 3 is prime.

1, 2, 3, 7, 19, 21, 31, 50, 55, 151, 167, 287, 542, 603, 926, 1046, 2066, 2139, 2651, 2787, 5756, 6028, 6925, 10135, 13037, 36476, 74234, 119295

Offset: 1

Author

Robert Price, Nov 09 2016

Keywords

• nonn
• more

Comments

For k > 0, numbers k such that the digits 88 followed by k-1 occurrences of the digit 0 followed by the digit 3 is prime (see Example section).

a(29) > 3*10^5.

Examples

			3 is in this sequence because 88*10^3 + 3 = 88003 is prime.
Initial terms and associated primes:
a(1) = 1, 883;
a(2) = 2, 8803;
a(3) = 3, 88003;
a(4) = 7, 880000003;
a(5) = 19, 880000000000000000003, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 880w3.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[88*10^# + 3] &] (* Corrected by Georg Fischer, Jul 22 2019 *)

PARI

is(n)=ispseudoprime(88*10^n + 3) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(28) from Robert Price, May 03 2020