This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A235661 #12 Feb 26 2025 19:40:47
%S A235661 2,3,5,11,19,29,37,41,53,61,71,89,131,137,149,157,233,263,271,281,293,
%T A235661 331,337,359,389,431,433,439,457,487,499,571,617,631,659,701,739,751,
%U A235661 761,809,859,877,907,911,1009,1019,1031,1033,1087,1093
%N A235661 Primes p with p*(p+1) - prime(p) prime.
%C A235661 This sequence is a subsequence of A235592.
%C A235661 By the conjecture in A232353, this sequence should have infinitely many terms.
%H A235661 Zhi-Wei Sun, <a href="/A235661/b235661.txt">Table of n, a(n) for n = 1..10000</a>
%e A235661 2 is a term because 2*3 - prime(2) = 3 is prime.
%e A235661 3 is a term because 3*4 - prime(3) = 7 is prime.
%e A235661 5 is a term because 5*6 - prime(5) = 19 is prime.
%t A235661 PQ[n_]:=PrimeQ[n(n+1)-Prime[n]]
%t A235661 n=0;Do[If[PQ[Prime[k]],n=n+1;Print[n," ",Prime[k]]],{k,1,1000}]
%t A235661 Select[Prime[Range[200]],PrimeQ[#(#+1)-Prime[#]]&] (* _Harvey P. Dale_, Feb 26 2025 *)
%Y A235661 Cf. A000040, A232353, A234695, A235592, A235613, A235614.
%K A235661 nonn
%O A235661 1,1
%A A235661 _Zhi-Wei Sun_, Jan 13 2014