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Numbers n such that n^3 is a sum of two successive primes.
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%I #14 Jun 05 2018 17:46:53

%S 2,6,28,42,72,162,174,220,222,234,246,252,296,344,380,390,486,510,584,

%T 594,638,646,674,702,720,816,828,882,942,948,990,1044,1056,1146,1200,

%U 1314,1422,1436,1554,1566,1596,1602,1632,1740,1770,1778,1806,1818,1824

%N Numbers n such that n^3 is a sum of two successive primes.

%C Prime(n)+ prime(n+1) as a square in A064397; n^2 as a sum of two successive primes in A074924; prime(n)+ prime(n+1) as a cube in A071220.

%H Chai Wah Wu, <a href="/A074925/b074925.txt">Table of n, a(n) for n = 1..10000</a> (terms for n = 1..429 from Zak Seidov)

%e 6^3 = 216 = 107 + 109.

%t Surd[#,3]&/@Select[Total/@Partition[Prime[Range[150*10^6]],2,1], IntegerQ[ Surd[#,3]]&] (* _Harvey P. Dale_, Jun 05 2018 *)

%o (Python)

%o from sympy import nextprime, prevprime

%o A074925_list = [i for i in range(2,10**4,2) if prevprime(i**3//2) + nextprime(i**3//2) == i**3] # _Chai Wah Wu_, Feb 22 2017

%Y Cf. A064397, A071220, A074924.

%K nonn

%O 1,1

%A _Zak Seidov_, Oct 02 2002

%E More terms from _Zak Seidov_, Jul 22 2009