A239476 Number of values of k such that 2^k + (6n+3) and (6n+3)*2^k - 1 are both prime, k < 6n+3.

2, 3, 5, 3, 7, 3, 1, 6, 2, 6, 6, 5, 4, 3, 2, 4, 5, 4, 1, 3, 2, 3, 3, 1, 7, 2, 2, 10, 1, 4, 1, 2, 4, 0, 3, 5, 1, 3, 4, 3, 5, 1, 5, 4, 6, 4, 2, 1, 2, 4, 4, 1, 5, 1, 4, 3, 2, 4, 3, 5, 6, 2, 6, 3, 2, 2, 2, 1, 4, 2, 1, 2, 3, 3, 4, 4, 4, 2, 3, 4, 7, 5, 2, 1, 4, 2, 1, 6, 2, 3, 2, 3, 5, 0, 5, 0, 0, 2, 2, 4, 4, 3

Offset: 0

Author

Ilya Lopatin and Juri-Stepan Gerasimov, Mar 20 2014

Keywords

• nonn

Comments

Number of values of k such that 2^k + A047263(n) and (A047263(n))*2^k + 1 are both prime, k < 6n+3, where A047263(n) is complement of 6m+3 : 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...

Examples

			a(0) = 2 because
1) 2^1 + (6*0+3) = 5 and (6*0+3)*2^1 - 1 = 5 for k = 1 < (6*0+3);
2) 2^2 + (6*0+3) = 7 and (6*0+3)*2^2 - 1 = 11 for k = 2 < (6*0+3).
a(1) = 3 because
1) 2^1 + (6*1+3) = 11 and (6*1+3)*2^1 - 1 = 17 for k = 1 < (6*1+3);
2) 2^3 + (6*1+3) = 17 and (6*1+3)*2^3 - 1 = 71 for k = 3 < (6*1+3);
3) 2^7 + (6*1+3) = 137 and (6*1+3)*2^7 - 1 = 1151 for k = 7 < (6*1+3).
a(2) = 5 because
1) 2^1 + (6*2+3) = 17 and (6*2+3)*2^1 - 1 = 29 for k = 1 < (6*2+3);
2) 2^2 + (6*2+3) = 19 and (6*2+3)*2^2 - 1 = 59 for k = 2 < (6*2+3);
3) 2^4 + (6*2+3) = 31 and (6*2+3)*2^4 - 1 = 239 for k = 4 < (6*2+3);
4) 2^5 + (6*2+3) = 37 and (6*2+3)*2^5 - 1 = 479 for k = 5 < (6*2+3);
5) 2^10 + (6*2+3) = 1039 and (6*2+3)*2^10 - 1 = 15359 for k = 10 < (3*2+3).
		

Crossrefs

Cf. A016945, A047263.

Programs

PARI

for(n=0, 100, 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 25 2014

Extensions

Offset changed to 0 by Colin Barker, Mar 25 2014