A239730 Number of values of k such that 2^k - (6n+3) and (6n+3)*2^k + 1 are both prime, k < 6n+3.

0, 0, 1, 3, 5, 3, 1, 3, 1, 5, 2, 1, 3, 2, 1, 1, 2, 5, 0, 3, 0, 1, 3, 2, 3, 2, 1, 5, 1, 1, 0, 0, 4, 1, 2, 2, 2, 2, 4, 1, 3, 1, 1, 3, 1, 4, 0, 1, 0, 2, 1, 0, 3, 0, 1, 2, 1, 3, 1, 3, 1, 1, 4, 2, 1, 1, 1, 4, 2, 2, 4, 3, 1, 1, 3, 4, 6, 4, 1, 1, 1, 1, 1, 1, 0, 5, 0, 2, 2, 2, 1, 1, 2, 1, 1, 0, 1, 1, 0, 2, 1, 0

Offset: 0

Author

Ilya Lopatin and Juri-Stepan Gerasimov, Mar 25 2014

Keywords

• nonn

Examples

			a(2) = 1 because
1) 2^10 - (6*2+3) = 1009 and (6*2+3)*2^10 + 1 = 15361 for k = 10 < (6*2+3).
a(3) = 3 because
1) 2^5 - (6*3+3) = 11 and (6*3+3)*2^5 + 1 = 673 for k = 5 < (6*3+3);
2) 2^7 - (6*3+3) = 107 and (6*3+3)*2^7 + 1 = 2689 for k = 7 < (6*3+3);
3) 2^9 - (6*3+3) = 491 and (6*3+3)*2^9 + 1 = 10753 for k = 9 < (6*3+3).
		

Crossrefs

Cf. A239476.

Programs

PARI

for(n=0, 120, m=0; for(k=0, 6*n+2, if(isprime(2^k-(6*n+3)) && isprime((6*n+3)*2^k+1), m++)); print1(m,", ")) \\ Colin Barker, Mar 26 2014

Extensions

a(24), a(76) and a(86) corrected by Colin Barker, Mar 26 2014