A210205 The sum of three consecutive prime numbers, beginning with a(n), is a cube.

439, 34603, 1016201, 3696493, 4002991, 6344687, 10221397, 14662309, 16209029, 19925483, 20856907, 22805969, 43441271, 60120691, 60761413, 62056457, 62710787, 87791567, 96268243, 125977651, 166225747, 170027449

Offset: 1

Author

Pablo Martínez, Mar 18 2012

Keywords

• nonn

Examples

			prime(85) + prime(86) + prime(87) = 439 + 443 + 449 = 1331 = 11^3.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A061308.

Programs

Mathematica

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 *)

Python

from _future_ import division
from sympy import nextprime, prevprime
A210205_list = []
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:
            A210205_list.append(p1)
        p1, p2, p3 = p2, p3, nextprime(p3)
        q = p1+p2+p3 # Chai Wah Wu, Dec 31 2015

Extensions

Extended by T. D. Noe, Mar 24 2012