A270831 Numbers k such that (7*10^k + 71)/3 is prime.

1, 2, 3, 4, 5, 7, 23, 29, 37, 39, 40, 89, 115, 189, 227, 253, 301, 449, 533, 607, 969, 1036, 1207, 1407, 1701, 3493, 7147, 11342, 21638, 22327, 25575, 25648, 34079, 39974, 47719, 49913, 74729, 100737, 103531, 168067

Offset: 1

Author

Robert Price, Mar 23 2016

Keywords

• nonn

Comments

For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 3 followed by the digits 57 is prime (see Example section).

a(41) > 2*10^5.

Examples

			3 is in this sequence because (7*10^3 + 71)/3 = 2357 is prime.
Initial terms and associated primes:
a(1) = 1, 47;
a(2) = 2, 257;
a(3) = 3, 2357;
a(4) = 4, 23357;
a(5) = 5, 233357, etc.
		

Links

• Makoto Kamada, Search for 23w57.

Crossrefs

Cf. A056654, A268448, A269303, A270339, A270613.

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[(7*10^# + 71)/3] &]

PARI

lista(nn) = {for(n=1, nn, if(ispseudoprime((7*10^n + 71)/3), print1(n, ", "))); } \\ Altug Alkan, Mar 23 2016

Extensions

a(38)-a(40) from Robert Price, May 21 2018