A382227 The smallest perfect cube which is a sum of n consecutive primes.

8, 1331, 19248832, 205379, 10648, 531441, 195112, 15069223, 175616, 68921, 9261000, 389017, 97336, 531441, 17173512, 68921, 343000, 30664297, 21952, 253636137, 3796416, 35611289, 8741816, 6859, 119095488, 12167, 110592, 11930499125, 1259712, 42508549, 373248, 4492125, 1560896, 10793861

Offset: 2

Author

David Dewan, Mar 19 2025

Keywords

• nonn

Comments

a(1) does not exist because no single prime is a perfect cube.

Examples

			a(2)=8        = 3 + 5.
a(3)=1331     = 439 + 443 + 449.
a(4)=19248832 = 4812191 + 4812193 + 4812209 + 4812239.
		

Links

• David Dewan, Table of n, a(n) for n = 2..200

Crossrefs

Cf. A382226, A382228, A132956.

Programs

Mathematica

a[n_]:=Do[mid=PrimePi[k^3/n]; toTest=Prime[Range[Max[mid-n,1],mid+n]]; t=Total/@Partition[toTest,n,1]; If[MemberQ[t,k^3],Return[k^3]],{k,2,Infinity}]; a/@Range[2, 10]

Formula

a(n) = A382228(n)^3.