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

2,1

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

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

Example

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).

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]

Crossrefs

Cf. A382227, A382228, A132955.

Sequence in context: A326373 A092052 A388650 * A139999 A140870 A157601

Adjacent sequences: A382223 A382224 A382225 * A382227 A382228 A382229

Keyword

nonn

Author

David Dewan, Mar 19 2025

Status

approved