This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A382228 #20 Mar 25 2025 10:23:02
%S A382228 2,11,268,59,22,81,58,247,56,41,210,73,46,81,258,41,70,313,28,633,156,
%T A382228 329,206,19,492,23,48,2285,108,349,72,165,116,221,236,187,44,1083,82,
%U A382228 295,34,347,54,35,548,23,32,2357,1170,37,632,813,1590,277,1972,177
%N A382228 Smallest k such that k^3 is the sum of n consecutive primes.
%C A382228 a(1) does not exist because no single prime is a perfect cube.
%H A382228 David Dewan, <a href="/A382228/b382228.txt">Table of n, a(n) for n = 2..200</a>
%F A382228 A382227(n) = a(n)^3.
%e A382228 a(2)=2 : 2^3 = 8 = 3 + 5.
%e A382228 a(3)=11 : 11^3 = 1331 = 439 + 443 + 449.
%e A382228 a(4)=268 : 268^3 = 19248832 = 4812191 + 4812193 + 4812209 + 4812239.
%t A382228 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]
%Y A382228 Cf. A000578, A382226, A382227, A132957
%K A382228 nonn
%O A382228 2,1
%A A382228 _David Dewan_, Mar 19 2025