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 A236242 #64 Aug 31 2019 12:47:20
%S A236242 5,6,7,8,12,13,19,69,91,102,116,119,171,198,216,222,278,299,338,584,
%T A236242 722,774,874,978,1004,1163,1268,1492,1836,1932,1966,2982,3508,3964,
%U A236242 4264,4894,5028,8236,8552,8639,12749,14017,14402,18150,18321,18514,18979,20935,21815,21828,21890,30734
%N A236242 Numbers m with C(2*m, m) + prime(m) prime, where C(2*m, m) = (2*m)!/(m!)^2.
%C A236242 According to the conjecture in A236241, this sequence should have infinitely many terms. The prime C(2*a(52),a(52)) + prime(a(52)) = C(61468, 30734) + prime(30734) has 18502 decimal digits.
%C A236242 For primes of the form C(2*m, m) + prime(m), see A236245.
%C A236242 See also A236248 for a similar sequence.
%H A236242 Zhi-Wei Sun, <a href="/A236242/b236242.txt">Table of n, a(n) for n = 1..52</a>
%H A236242 Zhi-Wei Sun, <a href="http://arxiv.org/abs/1402.6641">Problems on combinatorial properties of primes</a>, arXiv:1402.6641 [math.NT], 2014-2016.
%e A236242 a(1) = 5 since C(2*1,1) + prime(1) = 4, C(2*2,2) + prime(2) = 9, C(2*3,3) + prime(3) = 25 and C(2*4,4) + prime(4) = 77 are all composite, but C(2*5,5) + prime(5) = 252 + 11 = 263 is prime.
%t A236242 n=0;Do[If[PrimeQ[Binomial[2m,m]+Prime[m]],n=n+1;Print[n," ",m]],{m,1,10000}]
%t A236242 Select[Range[9000],PrimeQ[Binomial[2#,#]+Prime[#]]&] (* _Harvey P. Dale_, Jan 18 2016 *)
%Y A236242 Cf. A000040, A000984, A236241, A236245, A236248, A236249, A236256.
%K A236242 nonn
%O A236242 1,1
%A A236242 _Zhi-Wei Sun_, Jan 20 2014
%E A236242 a(41)-a(52) from bfile by _Robert Price_, Aug 31 2019