A248587 The smallest of four consecutive primes whose sum is a perfect cube.

4812191, 6353029, 8039333, 8821867, 19876711, 60742631, 85017061, 108879847, 127042367, 138853049, 170367959, 238190951, 259108427, 414949357, 485941193, 512095739, 529218559, 582868471, 623331491, 648485381, 771656657, 1001132351, 1098706507, 1172752457

Offset

1,1

Links

K. D. Bajpai and Chai Wah Wu, Table of n, a(n) for n = 1..10000 n = 1..42 from K. D. Bajpai.

Example

a(2) = 6353029 is prime. Next three primes are 6353033, 6353051 and 6353071. Their sum = 6353029 + 6353033 + 6353051 + 6353071 = 25412184 = 294^3.
a(3) = 8039333 is prime. Next three primes are 8039359, 8039363 and 8039377. Their sum = 8039333 + 8039359 + 8039363 + 8039377 = 32157432 = 318^3.

Mathematica

t = {}; p = 2; q = 3; r = 5; Do[v = NextPrime[r]; If[IntegerQ[(p + q + r + v)^(1/3)], AppendTo[t, p]; Print[p]]; p = q; q = r; r = v, {5*10^8}]; t
Select[Partition[Prime[Range[6*10^7]], 4, 1], IntegerQ[Surd[Total[#], 3]] &] [[All, 1]] (* Harvey P. Dale, Oct 07 2016 *)

Prog

(PARI) lista(nn) = {vp = primes(nn); for (i=1, #vp - 3, if (ispower(vp[i]+vp[i+1]+vp[i+2]+vp[i+3], 3), print1(vp[i], ", ")); ); } \\ Michel Marcus, Oct 24 2014
(Python)
from sympy import nextprime, prevprime
A248587_list = []
for i in range(3, 10**6):
    n = i**3
    p3 = prevprime(n//4)
    p2, p4 = prevprime(p3), nextprime(p3)
    p1 = prevprime(p2)
    q = p1+p2+p3+p4
    while q <= n:
        if q == n:
            A248587_list.append(p1)
        p1, p2, p3, p4 = p2, p3, p4, nextprime(p4)
        q = p1+p2+p3+p4 # Chai Wah Wu, Dec 31 2015

Crossrefs

Cf. A000040 (primes), A000578 (cubes).

Cf. A061308 (two consecutive primes), A210205 (three consecutive primes).

Sequence in context: A017503 A017635 A203655 * A204053 A176772 A017538

Adjacent sequences: A248584 A248585 A248586 * A248588 A248589 A248590

Keyword

nonn

Author

K. D. Bajpai, Oct 09 2014

Status

approved