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 A345665 #15 Dec 23 2024 22:56:48
%S A345665 4,6,7,9,11,13,16,19,22,25,28,30,33,36,40,43,46,49,52,55,58,62,66,70,
%T A345665 73,75,77,81,86,91,95,99,102,106,110,113,117,121,124,129,132,135,138,
%U A345665 142,147,153,158,162,165,167,171,175,179,184,188
%N A345665 Ceiling of circumradius of quadrilateral with consecutive prime sides configured as a cyclic quadrilateral.
%C A345665 The first cyclic quadrilateral in this sequence with sides (2,3,5,7) is analogous to an obtuse triangle in that the circumcenter does not lie within the bounds of the quadrilateral. Thereafter, the quadrilaterals have circumcenters that lie within the bounds of the quadrilateral.
%H A345665 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CyclicQuadrilateral.html">Cyclic Quadrilateral</a>.
%H A345665 Wikipedia, <a href="https://en.wikipedia.org/wiki/Cyclic_quadrilateral">Cyclic quadrilateral</a>.
%H A345665 Wikipedia, <a href="https://en.wikipedia.org/wiki/Prime_triplet">Prime triplet</a>.
%F A345665 The circumradius R of a cyclic quadrilateral with sides a, b, c, d is given by the Parameshvara's circumradius formula R = sqrt((a*b+c*d)*(a*c+b*d)*(a*d+b*c)/((s-a)*(s-b)*(s-c)*(s-d)))/4 where s = (a+b+c+d)/2.
%e A345665 a(2)=6 because a cyclic quadrilateral with sides (3,5,7,11) has circumradius = 5.56365...
%t A345665 lst = {}; Do[{a, b, c, d}={Prime[n], Prime[n+1], Prime[n+2], Prime[n+3]}; s=(a+b+c+d)/2; R=Sqrt[(a*b+c*d)(a*c+b*d)(a*d+b*c)/((s-a)(s-b)(s-c)(s-d))]/4; AppendTo[lst, Ceiling@R], {n, 1, 100}]; lst
%Y A345665 Cf. A329950, A331676.
%K A345665 nonn
%O A345665 1,1
%A A345665 _Frank M Jackson_, Jun 21 2021