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A109725
Divide primes in groups with 2n+1 elements and add together.
5
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
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
KEYWORD
easy,nonn
AUTHOR
Giovanni Teofilatto, Aug 10 2005
EXTENSIONS
Edited and extended by Ray Chandler, Aug 11 2005
STATUS
approved