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 A125270 #7 Sep 05 2014 17:39:59
%S A125270 1358,3954,10478,22210,43490,78014,129530,206650,324350,466270,621466,
%T A125270 853742,1132130,1436690,1870850,2388050,2886370,3440410,4133410,
%U A125270 4904906,5926654,7195670,8425430,9792950,11040910,12098990,13917898,16097810
%N A125270 Coefficient of x^2 in polynomial whose zeros are 5 consecutive primes starting with the n-th prime.
%C A125270 Sums of all distinct products of 3 out of 5 consecutive primes, starting with the n-th prime; value of 3rd elementary symmetric function on the 5 consecutive primes.
%F A125270 Let p = Prime(n), q = Prime(n+1), r = Prime(n+2), s = Prime(n+3) and t = Prime(n+4). Then a(n) = p q (r+s+t) + (p + q) r (s + t) + (p + q + r) s t.
%t A125270 a = {}; Do[AppendTo[a, (Prime[x] Prime[x + 1] Prime[x + 2] + Prime[x] Prime[x + 1] Prime[x + 3] + Prime[x] Prime[x + 1] Prime[x + 4] + Prime[x] Prime[x + 2] Prime[x + 3] + Prime[x] Prime[x + 2] Prime[x + 4] + Prime[x] Prime[x + 3] Prime[x + 4] + Prime[x + 1] Prime[x + 2] Prime[x + 3] + Prime[x + 1] Prime[x + 2] Prime[x + 4] + Prime[x + 1] Prime[x + 3] Prime[x + 4] + Prime[x + 2] Prime[x + 3] Prime[x + 4])], {x, 1, 100}]; a
%t A125270 fcp[{p_,q_,r_,s_,t_}]:=p*q(r+s+t)+(p+q)r(s+t)+(p+q+r)s*t; fcp/@Partition[ Prime[ Range[40]],5,1] (* _Harvey P. Dale_, Sep 05 2014 *)
%Y A125270 Cf. A001043, A034961, A034963, A034964, A127333, A127334, A127335, A127336, A127337, A127338, A127339, A127340, A127341, A127342, A127343, A127345, A127346, A127347, A127348, A127349, A127351, A037171, A034962, A034965, A082246, A082251, A070934, A006094, A046301, A046302, A046303, A046324, A046325, A046326, A046327, A127489.
%K A125270 nonn
%O A125270 1,1
%A A125270 _Artur Jasinski_, Jan 16 2007
%E A125270 Edited and corrected by _Franklin T. Adams-Watters_, Jan 23 2007