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

3,1

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

Formula

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

Mathematica

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

Crossrefs

Cf. A000040.

Partial sums of A024675.

Sequence in context: A025720 A022793 A005448 * A301247 A037040 A007077

Adjacent sequences: A373696 A373697 A373698 * A373700 A373701 A373702

Keyword

nonn,easy

Author

Paolo Xausa, Jun 17 2024

Status

approved