A353263 Primes whose square is the sum of the cubes of four primes, not necessarily distinct.
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
Keywords
Examples
1193 is a term because 2^3 + 29^3 + 47^3 + 109^3 = 1423249 = 1193^2.
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.
Programs
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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
Extensions
a(11) and beyond from Michael S. Branicky, Apr 09 2022
Comments