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%I #13 Apr 10 2020 11:34:31
%S 2,3,4,5,6,8,9,11,14,15,18,19,20,21,26,27,29,34,36,37,38,41,44,45,48,
%T 53,54,57,61,62,69,70,71,85,86,87,89,90,98,99,102,105,112,114,117,119,
%U 131,134,135,136,137,141,145,147,149,150,153,156,157,162,170,171,175,176,180,183,187,189,198,200
%N Numbers k such that k*(k+1) - prime(k) is prime.
%C It is known that prime(k) <= k*(k+1) for any positive integer k. The conjecture in A235613 implies that the sequence has infinitely many terms.
%C Conjecture: This sequence contains infinitely many primes.
%H Zhi-Wei Sun, <a href="/A235592/b235592.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1) = 2 since 1*2 - prime(1) = 0 is not prime, but 2*3 - prime(2) = 3 is prime.
%e a(2) = 3 since 3*4 - prime(3) = 7 is prime.
%e a(3) = 4 since 4*5 - prime(4) = 13 is prime.
%t n=0;Do[If[PrimeQ[k(k+1)-Prime[k]],n=n+1;Print[n," ",k]],{k,1,200}]
%t Select[Range[200],PrimeQ[(#(#+1))-Prime[#]]&] (* _Harvey P. Dale_, Apr 10 2020 *)
%Y Cf. A000040, A235613, A235614.
%K nonn
%O 1,1
%A _Zhi-Wei Sun_, Jan 12 2014
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