A271146 Numbers k such that (16*10^k - 19)/3 is prime.

1, 4, 5, 6, 10, 13, 20, 22, 24, 35, 41, 42, 46, 155, 222, 336, 432, 538, 577, 637, 679, 750, 758, 785, 2262, 5436, 6806, 7962, 9757, 16016, 24588, 47918, 59062, 74092, 81896, 85495, 102299, 185978, 190420

Offset: 1

Author

Robert Price, Mar 31 2016

Keywords

• nonn
• more

Comments

For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 3 followed by the digits 27 is prime (see Example section).

a(40) > 2*10^5.

Examples

			4 is in this sequence because (16*10^4 - 19)/3 = 53327 is prime.
Initial terms and associated primes:
a(1) = 1, 47;
a(2) = 4, 53327;
a(3) = 5, 533327;
a(4) = 6, 5333327;
a(5) = 10, 53333333327;
a(6) = 13, 53333333333327, etc.
		

Links

• Makoto Kamada, Search for 53w27.

Crossrefs

Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A270974.

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[(16*10^# - 19)/3] &]

PARI

lista(nn) = {for(n=1, nn, if(ispseudoprime((16*10^n - 19)/3), print1(n, ", ")));} \\ Altug Alkan, Mar 31 2016

Extensions

a(37)-a(39) from Robert Price, Feb 23 2019