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A353263
Primes whose square is the sum of the cubes of four primes, not necessarily distinct.
1
1193, 1949, 5639, 7907, 8501, 10301, 20101, 20939, 29137, 30091, 34403, 65173, 68567, 70249, 70537, 76801, 84163, 105943, 109147, 116483, 153247, 161753, 169943, 171733, 175829, 180563, 208589, 214483, 222197, 224969, 242483, 261427, 280507, 313933, 317327, 319883
OFFSET
1,1
COMMENTS
The sum must contain 2^3, else it will be even, hence not prime. - Michael S. Branicky, Apr 10 2022
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..724
Zhichun Zhai, Problems related to Waring-Goldbach problem involving cubes of primes, arXiv:2201.07346 [math.GM], 2022. See Table 2 p. 3. Warning 85012 is a typo for 8501.
EXAMPLE
1193 is a term because 2^3 + 29^3 + 47^3 + 109^3 = 1423249 = 1193^2.
PROG
(PARI) list(lim)=my(v=List(), P=apply(p->p^3, primes(sqrtnint(lim\=1, 3)))); foreach(P, p, foreach(P, q, foreach(P, r, my(s=p+q+r, t); for(i=1, #P, t=s+P[i]; if(t>lim, break); if (issquare(t, &rr) && isprime(rr), listput(v, rr)))))); v = Set(v); \\ after A346917
CROSSREFS
Square roots of the intersection of A346917 and A001248.
Cf. A353249.
Sequence in context: A103171 A032530 A344628 * A287049 A153379 A103172
KEYWORD
nonn
AUTHOR
Michel Marcus, Apr 09 2022
EXTENSIONS
a(11) and beyond from Michael S. Branicky, Apr 09 2022
STATUS
approved