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 A182365 #10 Apr 30 2012 15:11:14
%S A182365 13,19,31,43,53,61,73,103,113,131,139,157,173,193,199,251,271,293,313,
%T A182365 353,379,421,443,463,499,509,523,577,613,619,661,691,733,743,757,773,
%U A182365 811,829,859,883,911,953,971,997,1013,1039,1069,1093,1109,1123,1153
%N A182365 The largest prime in some interval of the form (2*prime(k),2*prime(k+1)) if this interval contains at least 2 primes.
%C A182365 These are called "left primes" in A166251.
%e A182365 For k=6 we have 2*13 < 29 < 31 < 2*17, and the interval contains two primes. Therefore 31 is in the sequence.
%t A182365 n = 0; t = {}; While[Length[t] < 100, n++; ps = Select[Range[2*Prime[n], 2*Prime[n + 1]], PrimeQ]; If[Length[ps] >= 2, AppendTo[t, ps[[-1]]]]]; t (* _T. D. Noe_, Apr 30 2012 *)
%Y A182365 Cf. A166252, A166251, A164368, A104272, A080359, A164333, A164288, A164294, A164554, A166307.
%K A182365 nonn
%O A182365 1,1
%A A182365 _Vladimir Shevelev_, Apr 26 2012