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A353249
Primes that are the sum of the cubes of four primes, not necessarily distinct.
1
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
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
KEYWORD
nonn
AUTHOR
Michel Marcus, Apr 08 2022
STATUS
approved