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%I #24 May 08 2018 17:52:20
%S 1331,103823,3048625,11089567,12008989,19034163,30664297,43986977,
%T 48627125,59776471,62570773,68417929,130323843,180362125,182284263,
%U 186169411,188132517,263374721,288804781,377933067,498677257,510082399,594823321,697864103,716917375
%N Cubes which are sum of three consecutive primes.
%H Donovan Johnson, <a href="/A227475/b227475.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = (A076306(n))^3. - _R. J. Mathar_, Sep 02 2013
%e a(2) = 103823 because prime(3696) + prime(3697) + prime(3698) = 34603 + 34607 + 34613 = 103823 = 47^3.
%t Select[Total[#]&/@Partition[Prime[Range[132*10^5]],3,1],IntegerQ[ Surd[ #,3]]&] (* _Harvey P. Dale_, May 08 2018 *)
%o (PARI) n=0; forstep(j=3, 86231, 2, c=j^3; c3=c/3; f=0; if(denominator(c3)==1, if(isprime(c3), if(precprime(c3-1)+c3+nextprime(c3+1)==c, f=1))); p2=precprime(c3); p1=precprime(p2-1); p3=nextprime(c3); p4=nextprime(p3+1); if(p1+p2+p3==c, f=1); if(p2+p3+p4==c, f=1); if(f==1, n++; write("b227475.txt", n " " c))) /* _Donovan Johnson_, Sep 02 2013 */
%Y Cf. A076306, A210205, A158796, A226524.
%K nonn
%O 1,1
%A _K. D. Bajpai_, Sep 02 2013
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