A353249 Primes that are the sum of the cubes of four primes, not necessarily distinct.

89, 149, 367, 383, 503, 601, 1709, 2221, 2357, 4001, 4937, 5171, 6599, 6883, 7019, 7237, 7243, 7583, 9091, 10177, 11261, 11807, 14747, 15923, 16693, 17431, 24413, 24767, 25673, 26539, 27059, 30169, 32587, 34739, 43517, 48731, 51031, 51347, 53201, 53323, 53699, 54133, 59617

Offset

1,1

Links

Table of n, a(n) for n=1..43.

Zhichun Zhai, Problems related to Waring-Goldbach problem involving cubes of primes, arXiv:2201.07346 [math.GM], 2022. See Table 1 p. 3 but some terms are missing.

Example

89 is a term because 2^3 + 3^3 + 3^3 + 3^3 = 89.
15923 is a term because 2^3 + 13^3 + 19^3 + 19^3 = 15923.

Maple

q:= proc(n, t) option remember; `if`(n=0, is(t=0), t>0 and
      ormap(p-> isprime(p) and q(n-p^3, t-1), [$2..iroot(n, 3)]))
    end:
select(x-> isprime(x) and q(x, 4), [$1..60000])[];  # Alois P. Heinz, Apr 08 2022

Mathematica

seq[max_] := Module[{s = Select[Range[Floor@Surd[max, 3]], PrimeQ]}, Select[Union[Plus @@@ (Tuples[s, 4]^3)], # <= max && PrimeQ[#] &]]; seq[60000] (* Amiram Eldar, Apr 08 2022 *)

Prog

(PARI) isok(p) = {if (isprime(p) && (p > 24), my(P=primes(primepi(sqrtn(p-24, 3)+1))); for (i=1, #P, for (j=i, #P, for (k=j, #P, for (n=k, #P, if (P[i]^3 + P[j]^3 + P[k]^3 + P[n]^3 == p, return (1)); ); ); ); ); ); }

Crossrefs

Primes in A346917.

Cf. A123597.

Sequence in context: A267819 A031416 A340307 * A247114 A075589 A142031

Adjacent sequences: A353246 A353247 A353248 * A353250 A353251 A353252

Keyword

nonn

Author

Michel Marcus, Apr 08 2022

Status

approved