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 A051735 #6 Dec 10 2015 17:05:48
%S A051735 6,462,1877405874732108,38650751381832,10000119226331142599460,
%T A051735 51913710643776705684835560,42552226353687619569660660,
%U A051735 1656627950725900171898183550,315676747963758694790502389846048040560005901701920,3571770735028382091998706667681023581492775768
%N A051735 Binomial coefficients C(n,k) such that C(n,k)-1 and C(n,k)+1 are twin primes and 2<=k<=floor(n/2).
%C A051735 Sequence is ordered by size of n not size of C(n,k). Link gives list of all values up to n=1352.
%H A051735 <a href="http://science.kennesaw.edu/~jdemaio/twinbc.htm">More terms</a>
%e A051735 C(11,5)=462 is a member of the sequence because 461 and 463 are twin primes.
%t A051735 Select[Flatten[Table[Binomial[n,k],{n,200},{k,2,Floor[n/2]}]], AllTrue[ #+ {1,-1},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Dec 10 2015 *)
%Y A051735 See A051770 for values of n, A051771 for values of k.
%K A051735 nonn
%O A051735 0,1
%A A051735 Joe DeMaio (jdemaio(AT)kennesaw.edu), Dec 06 1999
%E A051735 More terms from _Harvey P. Dale_, Dec 10 2015