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A235681 Primes p with prime(p) - p + 1 and p*(p+1) - prime(p) both prime.

%I A235681 #9 Jan 13 2014 16:51:46
%S A235681 2,3,5,41,61,71,89,271,281,293,337,499,571,751,907,911,1093,1531,2027,
%T A235681 2341,2707,2861,3011,3359,3391,3511,4133,5179,5189,5483,5573,5657,
%U A235681 5867,6577,6827,7159,7411,7753,7879,8179,8467,9209,9391,9419,9433,10259,10303,10859,10993,11287
%N A235681 Primes p with prime(p) - p + 1 and p*(p+1) - prime(p) both prime.
%C A235681 This is the intersection of A234695 and A235661. For any prime p in this sequence, p^2 + 1 is the sum of the two primes prime(p) - p + 1 and p*(p+1) - prime(p).
%C A235681 By the conjecture in A235682, this sequence should have infinitely many terms.
%H A235681 Zhi-Wei Sun, <a href="/A235681/b235681.txt">Table of n, a(n) for n = 1..10000</a>
%e A235681 a(1) = 2 since prime(2) - 2 + 1 = 2 and 2*3 - prime(2) = 3 are both prime.
%e A235681 a(2) = 3 since prime(3) - 3 + 1 = 3 and 3*4 - prime(3) = 7 are both prime.
%e A235681 a(3) = 5 since prime(5) - 5 + 1 = 7 and 5*6 - prime(5) = 19 are both prime.
%t A235681 PQ[n_]:=PrimeQ[Prime[n]-n+1]&&PrimeQ[n(n+1)-Prime[n]]
%t A235681 n=0;Do[If[PQ[Prime[k]],n=n+1;Print[n," ",Prime[k]]],{k,1,1000}]
%Y A235681 Cf. A000040, A234694, A234695,  A232353, A235189, A235330, A235613, A235614, A235661, A235682.
%K A235681 nonn
%O A235681 1,1
%A A235681 _Zhi-Wei Sun_, Jan 13 2014