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

2,1

Comments

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

Links

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

Formula

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

Example

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.

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]

Crossrefs

Cf. A000578, A382226, A382227, A132957

Sequence in context: A134096 A132571 A102031 * A248865 A072386 A185122

Adjacent sequences: A382225 A382226 A382227 * A382229 A382230 A382231

Keyword

nonn

Author

David Dewan, Mar 19 2025

Status

approved