A382226 -id:A382226 - cp's OEIS frontend

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

David Dewan, Mar 19 2025

nonn

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

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

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

Cf. A382226, A382228, A132956.

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]

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

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

Original entry on oeis.org

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

David Dewan, Mar 19 2025

nonn

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

			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.

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

Cf. A000578, A382226, A382227, A132957

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]

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

cp's OEIS Frontend

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

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