|
%I #6 Jan 15 2014 20:32:41
%S 7,11,19,23,41,73,83,109,197,211,229,271,379,461,541,631,641,659,859,
%T 991,1031,1049,1051,1093,1103,1217,1429,1451,1879,2063,2131,2287,2341,
%U 2411,3019,3257,3461,3659,3673,3691,3709,3917,3967,4409,4463,4519,5279,5303,5471,5477
%N Odd primes p with (p^2 - 1)/4 - prime((p - 1)/2) and (p^2 - 1)/4 + prime((p - 1)/2) both prime.
%C By the conjecture in A235728, this sequence should have infinitely many terms.
%H Zhi-Wei Sun, <a href="/A235727/b235727.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1) = 7 since neither (3^2-1)/4 - prime((3-1)/2) = 1 nor (5^2-1)/4 + prime((5-1)/2) = 9 is prime, but (7^2-1)/4 - prime((7-1)/2) = 12 - 5 = 7 and (7^2-1)/4 + prime((7-1)/2) = 12 + 5 = 17 are both prime.
%t q[n_]:=q[n]=PrimeQ[n(n+1)-Prime[n]]&&PrimeQ[n(n+1)+Prime[n]]
%t n=0;Do[If[q[(Prime[k]-1)/2],n=n+1;Print[n," ",Prime[k]]],{k,2,1000}]
%Y Cf. A000040, A232353, A235592, A235661, A235681, A235682, A235703, A235728.
%K nonn
%O 1,1
%A _Zhi-Wei Sun_, Jan 15 2014
|
