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A210205
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The sum of three consecutive prime numbers, beginning with a(n), is a cube.
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3
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439, 34603, 1016201, 3696493, 4002991, 6344687, 10221397, 14662309, 16209029, 19925483, 20856907, 22805969, 43441271, 60120691, 60761413, 62056457, 62710787, 87791567, 96268243, 125977651, 166225747, 170027449
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OFFSET
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1,1
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LINKS
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EXAMPLE
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prime(85) + prime(86) + prime(87) = 439 + 443 + 449 = 1331 = 11^3.
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MATHEMATICA
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t = {}; p = 2; q = 3; Do[r = NextPrime[q]; If[IntegerQ[(p + q + r)^(1/3)], AppendTo[t, p]; Print[p]]; p = q; q = r, {1000000}]; t (* T. D. Noe, Mar 24 2012 *)
Select[Partition[Prime[Range[9505000]], 3, 1], IntegerQ[Surd[Total[#], 3]]&][[All, 1]] (* Harvey P. Dale, May 22 2020 *)
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PROG
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(Python)
from __future__ import division
from sympy import nextprime, prevprime
for i in range(3, 10**6):
n = i**3
p2 = prevprime(n//3)
p1, p3 = prevprime(p2), nextprime(p2)
q = p1+p2+p3
while q <= n:
if q == n:
p1, p2, p3 = p2, p3, nextprime(p3)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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