A382228 -id:A382228 - cp's OEIS frontend

A382226 Smallest prime in a sequence of n consecutive primes which add to a perfect cube.

3, 439, 4812191, 41051, 1753, 75869, 24359, 1674289, 17509, 6221, 771653, 29863, 6899, 35353, 1073239, 4001, 18959, 1613741, 1033, 12077759, 172433, 1548149, 364079, 199, 4580399, 373, 3847, 411396253, 41863, 1371031, 11491, 135911, 45707, 308149, 364909, 176537, 2089, 32569961, 13619, 625861

Offset: 2

David Dewan, Mar 19 2025

nonn

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

			a(2)=3  :       3 + 5 = 8 = 2^3 = A382227(2).
a(3)=439 :      439 + 443 + 449 = 1331 = 11^3 = A382227(3) = A210205(1).
a(4)=4812191 :   4812191 + 4812193 + 4812209 + 4812239 = 19248832 = 268^3 = A382227(4) = A248587(1).

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

Cf. A382227, A382228, A132955.

A382226 := proc(n)
        local i,ps,fp,lp ;
        fp := 2;
        ps := add(ithprime(j),j=1..n) ;
        lp := ithprime(n);
        for i from 1 do
                if isA000578(ps) then #code in A000578
                        return fp;
                end if;
                lp := nextprime(lp) ;
                ps := ps-fp+lp ;
                fp := nextprime(fp) ;
        end do:
end proc:
for n from 2 do
        print(n,A382226(n)) ;
end do:  # R. J. Mathar, Mar 25 2025

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

a(n) = { min prime(k): [ sum(j=k..k+n-1) prime(j)] in A000578 }.

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

Original entry on oeis.org

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.

cp's OEIS Frontend

A382226 Smallest prime in a sequence of n consecutive primes which add to a perfect cube.

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