A109725 Divide primes in groups with 2n+1 elements and add together.

2, 15, 83, 281, 679, 1367, 2461, 4005, 6223, 9017, 12755, 17281, 22967, 29597, 37793, 47229, 57993, 70957, 85343, 101777, 119469, 141079, 163313, 188201, 216203, 247203, 280897, 316551, 355905, 398825, 445509, 494953, 549737, 605711, 665185, 730353, 801481

Offset: 0

Author

Giovanni Teofilatto, Aug 10 2005

Keywords

• easy
• nonn

Comments

First difference of A109724.

Links

• Ray Chandler, Table of n, a(n) for n = 0..9999

Crossrefs

Cf. A007504, A109722-A109726.

Programs

Mathematica

f[n_] := Sum[Prime[k], {k, n}]; Table[f[(n+1)^2] - f[n^2], {n, 0, 34}]
With[{nn=40},Total/@TakeList[Prime[Range[nn^2]],Range[1,2nn-1,2]]] (* Requires Mathematica version 11 or later *) (* Harvey P. Dale, Jan 05 2019 *)

Python

from sympy import prime
def a(n): return sum(prime(i) for i in range(n*n+1, (n+1)**2+1))
print([a(n) for n in range(37)]) # Michael S. Branicky, Feb 15 2021

Formula

a(n) = A109724(n+1) - A109724(n) = A007504((n+1)^2) - A007504(n^2).

Extensions

Edited and extended by Ray Chandler, Aug 11 2005