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
Keywords
Examples
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.
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.
Programs
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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 *) -
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)););););););}
Comments