A382228 Smallest k such that k^3 is the sum of n consecutive primes.

2, 11, 268, 59, 22, 81, 58, 247, 56, 41, 210, 73, 46, 81, 258, 41, 70, 313, 28, 633, 156, 329, 206, 19, 492, 23, 48, 2285, 108, 349, 72, 165, 116, 221, 236, 187, 44, 1083, 82, 295, 34, 347, 54, 35, 548, 23, 32, 2357, 1170, 37, 632, 813, 1590, 277, 1972, 177

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)=2 :    2^3 = 8 = 3 + 5.
a(3)=11 :   11^3 = 1331 = 439 + 443 + 449.
a(4)=268 :  268^3 = 19248832 = 4812191 + 4812193 + 4812209 + 4812239.
		

Links

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

Crossrefs

Cf. A000578, A382226, A382227, A132957

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]], {k,2,Infinity}]; a/@Range[2, 10]

Formula

A382227(n) = a(n)^3.