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 A131019 #15 Feb 16 2025 08:33:06
%S A131019 13,18,24,30,36,44,51,60,69,76,84,92,101,110,120,129,136,145,153,162,
%T A131019 174,185,195,204,210,216,228,240,254,267,278,288,298,310,319,330,341,
%U A131019 350,362,372,381,390,400,415,430,445,456,464,471,482,494,506,520,530
%N A131019 Semiperimeters of quadrilaterals whose sides are 4 consecutive odd primes.
%C A131019 (2+3+5+7)/2 = 8.5, not an integer. Hence we restrict to odd primes. The cyclic quadrilaterals whose areas, rounded, are prime are given in A131020. The prime semiperimeters begin: a(1) = 13, a(13) = 101. This arises in the cyclic quadrilateral analog of A106171.
%D A131019 Coxeter, H. S. M. and Greitzer, S. L. "Cyclic Quadrangles; Brahmagupta's Formula", Sect. 3.2 in Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 56-60, 1967.
%H A131019 J. L. Coolidge, <a href="http://www.jstor.org/stable/2302891">A Historically Interesting Formula for the Area of a Quadrilateral</a>, Amer. Math. Monthly 46, 345-347, 1939.
%H A131019 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BrahmaguptasFormula.html">Brahmagupta's Formula.</a>
%F A131019 a(n) = (prime(n) + prime(n+1) + prime(n+2) + prime(n+3))/2 for n>1.
%F A131019 a(n) = (prime(n+1) + prime(n+2) + prime(n+3) + prime(n+4))/2 = A034963(n)/2.
%e A131019 a(1) = (3 + 5 + 7 + 11)/2 = 13.
%p A131019 A131019 := proc(n) local i ; add( ithprime(n+i),i=1..4)/2 ; end: for n from 1 to 180 do printf("%d, ",A131019(n)) : od:
%t A131019 Plus@@@Partition[Prime[Range[2,6! ]],4,1]/2 (* _Vladimir Joseph Stephan Orlovsky_, Feb 18 2010 *)
%Y A131019 Cf. A106171, A131020.
%Y A131019 Cf. A034963.
%K A131019 nonn
%O A131019 1,1
%A A131019 _Jonathan Vos Post_, Jun 09 2007
%E A131019 Edited by _R. J. Mathar_, Jun 12 2007