A353263 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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

Adjacent sequences: A353260 A353261 A353262 * A353264 A353265 A353266

KEYWORD

nonn

AUTHOR

Michel Marcus, Apr 09 2022

EXTENSIONS

a(11) and beyond from Michael S. Branicky, Apr 09 2022

STATUS

approved