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a(n) is the area of the (n+1)-gon having vertices coordinates (2,0), (2,prime(2)), ..., (n,prime(n)), (n,0).
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%I #10 Jun 17 2024 18:36:56

%S 4,10,19,31,46,64,85,111,141,175,214,256,301,351,407,467,531,600,672,

%T 748,829,915,1008,1107,1209,1314,1422,1533,1653,1782,1916,2054,2198,

%U 2348,2502,2662,2827,2997,3173,3353,3539,3731,3926,4124,4329,4546,4771,4999,5230

%N a(n) is the area of the (n+1)-gon having vertices coordinates (2,0), (2,prime(2)), ..., (n,prime(n)), (n,0).

%C In other words, area between the polyline (2,prime(2)), (3,prime(3)), ..., (n,prime(n)) and the x axis.

%H Paolo Xausa, <a href="/A373699/b373699.txt">Table of n, a(n) for n = 3..10000</a>

%F a(n) = Sum_{k=1..n-2} A024675(k).

%t Accumulate[Most[#] + Differences[#]/2] & [Prime[Range[2, 100]]]

%Y Cf. A000040.

%Y Partial sums of A024675.

%K nonn,easy

%O 3,1

%A _Paolo Xausa_, Jun 17 2024