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 A210205 The sum of three consecutive prime numbers, beginning with a(n), is a cube. 3
 439, 34603, 1016201, 3696493, 4002991, 6344687, 10221397, 14662309, 16209029, 19925483, 20856907, 22805969, 43441271, 60120691, 60761413, 62056457, 62710787, 87791567, 96268243, 125977651, 166225747, 170027449 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Chai Wah Wu, Table of n, a(n) for n = 1..10000 EXAMPLE prime(85) + prime(86) + prime(87) = 439 + 443 + 449 = 1331 = 11^3. 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 *) PROG (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 CROSSREFS Cf. A061308. Sequence in context: A157737 A061328 A177489 * A092048 A296905 A279812 Adjacent sequences:  A210202 A210203 A210204 * A210206 A210207 A210208 KEYWORD nonn AUTHOR Pablo MartÃ­nez, Mar 18 2012 EXTENSIONS Extended by T. D. Noe, Mar 24 2012 STATUS approved

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Last modified August 11 00:32 EDT 2020. Contains 336403 sequences. (Running on oeis4.)