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

0,1

Comments

First difference of A109724.

Links

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

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A007504, A109722-A109726.

Sequence in context: A215705 A368783 A301566 * A057152 A002740 A178750

Adjacent sequences: A109722 A109723 A109724 * A109726 A109727 A109728

Keyword

easy,nonn

Author

Giovanni Teofilatto, Aug 10 2005

Extensions

Edited and extended by Ray Chandler, Aug 11 2005

Status

approved