A227475 Cubes which are sum of three consecutive primes.

1331, 103823, 3048625, 11089567, 12008989, 19034163, 30664297, 43986977, 48627125, 59776471, 62570773, 68417929, 130323843, 180362125, 182284263, 186169411, 188132517, 263374721, 288804781, 377933067, 498677257, 510082399, 594823321, 697864103, 716917375

Offset: 1

Author

K. D. Bajpai, Sep 02 2013

Keywords

• nonn

Examples

			a(2) = 103823 because prime(3696) + prime(3697) + prime(3698) = 34603 + 34607 + 34613 = 103823 = 47^3.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A076306, A210205, A158796, A226524.

Programs

Mathematica

Select[Total[#]&/@Partition[Prime[Range[132*10^5]],3,1],IntegerQ[ Surd[ #,3]]&] (* Harvey P. Dale, May 08 2018 *)

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 */

Formula

a(n) = (A076306(n))^3. - R. J. Mathar, Sep 02 2013