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 A127350 #11 May 27 2025 18:27:17
%S A127350 288,574,1078,1750,2710,4006,5590,7630,10270,13030,15766,19462,23510,
%T A127350 27550,32830,38590,43750,49190,55570,62302,70726,80470,89350,98710,
%U A127350 106870,113590,124822,137590,151990,167230,186454,199798,214774,230270,247630,262942,281422
%N A127350 a(n) = Sum_{i=n..n+3} Sum_{j=i+1..n+4} prime(i)*prime(j).
%C A127350 a(n) = absolute value of the coefficient of x^3 of the polynomial Prod_{j=0,4}(x-prime(n+j)) of degree 5; the roots of this polynomial are prime(n), ..., prime(n+4); cf. Vieta's formulas.
%C A127350 All terms are even.
%H A127350 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/VietasFormulas.html">Vieta's Formulas</a>
%t A127350 Table[Prime[x] Prime[x + 1] + Prime[x] Prime[x + 2] + Prime[x] Prime[x + 3] + Prime[x] Prime[x + 4] + Prime[x + 1] Prime[x + 2] + Prime[x + 1] Prime[x + 3] + Prime[x + 1] Prime[x + 4] + Prime[x + 2] Prime[x + 3] + Prime[x + 2] Prime[x + 4] + Prime[x + 3] Prime[x + 4], {x, 1, 100}]
%o A127350 (PARI) {m=34;k=4;for(n=1,m,print1(sum(i=n,n+k-1,sum(j=i+1,n+k,prime(i)*prime(j))),","))} \\ _Klaus Brockhaus_, Jan 21 2007
%o A127350 (PARI) {m=34;k=4;for(n=1,m,print1(abs(polcoeff(prod(j=0,k,(x-prime(n+j))),3)),","))} \\ _Klaus Brockhaus_, Jan 21 2007
%Y A127350 Cf. A000040, A127345, A127346, A127347, A127348, A127349, A127351, A070934, A006094.
%K A127350 nonn
%O A127350 1,1
%A A127350 _Artur Jasinski_, Jan 11 2007
%E A127350 Edited by _Klaus Brockhaus_, Jan 21 2007