A373699 a(n) is the area of the (n+1)-gon having vertices coordinates (2,0), (2,prime(2)), ..., (n,prime(n)), (n,0).

4, 10, 19, 31, 46, 64, 85, 111, 141, 175, 214, 256, 301, 351, 407, 467, 531, 600, 672, 748, 829, 915, 1008, 1107, 1209, 1314, 1422, 1533, 1653, 1782, 1916, 2054, 2198, 2348, 2502, 2662, 2827, 2997, 3173, 3353, 3539, 3731, 3926, 4124, 4329, 4546, 4771, 4999, 5230

Offset: 3

Author

Paolo Xausa, Jun 17 2024

Keywords

• nonn
• easy

Comments

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

Links

• Paolo Xausa, Table of n, a(n) for n = 3..10000

Crossrefs

Cf. A000040.

Partial sums of A024675.

Programs

Mathematica

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

Formula

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