%I #7 Apr 27 2021 18:53:24
%S 5,12,18,45,36,75,54,105,182,90,238,195,126,225,350,392,180,448,345,
%T 216,532,405,602,837,495,306,525,324,555,1800,645,938,414,1584,450,
%U 1078,1120,825,1190,1232,540,2046,576,975,594,2665,2821,1125,684,1155,1652
%N Sums of two consecutive primes and composite numbers in-between.
%F a(n) = Sum_{k=prime(n)..prime(n+1)} k. - _Wesley Ivan Hurt_, Apr 27 2021
%t f[n_,x_]:=n*x+x*(x+1)/2;Table[Prime[n]+f[Prime[n],Prime[n+1]-Prime[n]-1]+Prime[n+1],{n,5!}]
%Y Cf. A034962, A054265.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Mar 21 2010