A270974 Numbers k such that 7*10^k + 57 is prime.

1, 2, 3, 5, 6, 7, 12, 14, 19, 21, 27, 33, 60, 61, 91, 102, 535, 549, 614, 695, 709, 1014, 2448, 2519, 3464, 3511, 6348, 6841, 11009, 11177, 20754, 26610, 30651, 39246, 122294

Offset: 1

Author

Robert Price, Mar 27 2016

Keywords

• nonn
• more

Comments

For k > 1, numbers k such that the digit 7 followed by k-2 occurrences of the digit 0 followed by the digits 57 is prime (see Example section).

a(35) > 2*10^5.

Examples

			3 is in this sequence because 7*10^3+57 = 7057 is prime.
Initial terms and associated primes:
a(1) = 1, 127;
a(2) = 2, 757;
a(3) = 3, 7057;
a(4) = 5, 700057;
a(5) = 6, 7000057;
a(6) = 7, 70000057, etc.
		

Links

• Makoto Kamada, Search for 70w57.

Crossrefs

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

Programs

Magma

[n: n in [1..500] | IsPrime(7*10^n + 57)]; // Vincenzo Librandi, Jul 03 2016

Mathematica

Select[Range[0, 100000], PrimeQ[7*10^# + 57] &]

PARI

lista(nn) = {for(n=1, nn, if(ispseudoprime(7*10^n + 57), print1(n, ", ")));} \\ Altug Alkan, Mar 27 2016

Extensions

a(35) from Robert Price, Jun 13 2019