cp's OEIS Frontend

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

%I A239476 #25 Apr 06 2014 04:20:16
%S A239476 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,
%T A239476 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,
%U A239476 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
%N A239476 Number of values of k such that 2^k + (6n+3) and (6n+3)*2^k - 1 are both prime, k < 6n+3.
%C A239476 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, ...
%e A239476 a(0) = 2 because
%e A239476 1) 2^1 + (6*0+3) = 5 and (6*0+3)*2^1 - 1 = 5 for k = 1 < (6*0+3);
%e A239476 2) 2^2 + (6*0+3) = 7 and (6*0+3)*2^2 - 1 = 11 for k = 2 < (6*0+3).
%e A239476 a(1) = 3 because
%e A239476 1) 2^1 + (6*1+3) = 11 and (6*1+3)*2^1 - 1 = 17 for k = 1 < (6*1+3);
%e A239476 2) 2^3 + (6*1+3) = 17 and (6*1+3)*2^3 - 1 = 71 for k = 3 < (6*1+3);
%e A239476 3) 2^7 + (6*1+3) = 137 and (6*1+3)*2^7 - 1 = 1151 for k = 7 < (6*1+3).
%e A239476 a(2) = 5 because
%e A239476 1) 2^1 + (6*2+3) = 17 and (6*2+3)*2^1 - 1 = 29 for k = 1 < (6*2+3);
%e A239476 2) 2^2 + (6*2+3) = 19 and (6*2+3)*2^2 - 1 = 59 for k = 2 < (6*2+3);
%e A239476 3) 2^4 + (6*2+3) = 31 and (6*2+3)*2^4 - 1 = 239 for k = 4 < (6*2+3);
%e A239476 4) 2^5 + (6*2+3) = 37 and (6*2+3)*2^5 - 1 = 479 for k = 5 < (6*2+3);
%e A239476 5) 2^10 + (6*2+3) = 1039 and (6*2+3)*2^10 - 1 = 15359 for k = 10 < (3*2+3).
%o A239476 (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
%Y A239476 Cf. A016945, A047263.
%K A239476 nonn
%O A239476 0,1
%A A239476 _Ilya Lopatin_ and _Juri-Stepan Gerasimov_, Mar 20 2014
%E A239476 Offset changed to 0 by _Colin Barker_, Mar 25 2014