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

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)=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).
		

Links

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

Crossrefs

Cf. A382227, A382228, A132955.

Programs

Maple

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

Mathematica

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]

Formula

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