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

%I A210205 #21 May 22 2020 19:59:34
%S A210205 439,34603,1016201,3696493,4002991,6344687,10221397,14662309,16209029,
%T A210205 19925483,20856907,22805969,43441271,60120691,60761413,62056457,
%U A210205 62710787,87791567,96268243,125977651,166225747,170027449
%N A210205 The sum of three consecutive prime numbers, beginning with a(n), is a cube.
%H A210205 Chai Wah Wu, <a href="/A210205/b210205.txt">Table of n, a(n) for n = 1..10000</a>
%e A210205 prime(85) + prime(86) + prime(87) = 439 + 443 + 449 = 1331 = 11^3.
%t A210205 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 *)
%t A210205 Select[Partition[Prime[Range[9505000]],3,1],IntegerQ[Surd[Total[#],3]]&][[All,1]] (* _Harvey P. Dale_, May 22 2020 *)
%o A210205 (Python)
%o A210205 from __future__ import division
%o A210205 from sympy import nextprime, prevprime
%o A210205 A210205_list = []
%o A210205 for i in range(3,10**6):
%o A210205     n = i**3
%o A210205     p2 = prevprime(n//3)
%o A210205     p1, p3 = prevprime(p2), nextprime(p2)
%o A210205     q = p1+p2+p3
%o A210205     while q <= n:
%o A210205         if q == n:
%o A210205             A210205_list.append(p1)
%o A210205         p1, p2, p3 = p2, p3, nextprime(p3)
%o A210205         q = p1+p2+p3 # _Chai Wah Wu_, Dec 31 2015
%Y A210205 Cf. A061308.
%K A210205 nonn
%O A210205 1,1
%A A210205 _Pablo Martínez_, Mar 18 2012
%E A210205 Extended by _T. D. Noe_, Mar 24 2012