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

1,1

Links

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

Formula

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

Example

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

Mathematica

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

Prog

(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 */

Crossrefs

Cf. A076306, A210205, A158796, A226524.

Sequence in context: A017391 A017655 A209844 * A036528 A052052 A122659

Adjacent sequences: A227472 A227473 A227474 * A227476 A227477 A227478

Keyword

nonn

Author

K. D. Bajpai, Sep 02 2013

Status

approved