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 A138205 #4 Mar 30 2012 17:22:47
%S A138205 0,1,2,1,4,5,10,7,0,1,16,5,10,1,2,13,22,23,0,19,20,37,40,23,16,0,0,25,
%T A138205 16,0,58,7,2,0,4,5,58,7,0,7,16,23,22,13,2,13,28,5,0,49,56,7,0,53,94,
%U A138205 31,2,7,46,71,46,7,32,31,4,65,28,13,26,31,58,47,88,1,14,73,0,5,28,49,8,37
%N A138205 Least number k such that n^2+k and n^2+k+2 are the smallest twin primes between squares n^2 and (n+1)^2, or 0 if there is no such k.
%C A138205 Checking up to n=10^6, it appears that a(n)=0 for only n=1 and the n in A091592.
%H A138205 T. D. Noe, <a href="/A138205/b138205.txt">Table of n, a(n) for n=1..10000</a>
%e A138205 a(7)=10 because (59,61) is the smallest twin-prime pair between 49 and 64.
%t A138205 Table[n2=n^2; k=1; While[k<2n+1 && !(PrimeQ[n2+k] && PrimeQ[n2+k+2]), k++ ]; If[k==2n+1,0,k], {n,10^4}]
%Y A138205 Cf. A091591 (number of twin prime pairs between n^2 and (n+1)^2).
%K A138205 nonn
%O A138205 1,3
%A A138205 _T. D. Noe_, Mar 06 2008