A193141 Primes that are the sum of 5 distinct positive cubes.

433, 443, 541, 673, 719, 827, 829, 881, 947, 953, 1171, 1217, 1223, 1277, 1289, 1297, 1559, 1583, 1609, 1619, 1709, 1747, 1801, 1861, 1871, 1879, 1889, 1973, 2003, 2017, 2081, 2087, 2131, 2137, 2141, 2213, 2221, 2251, 2269, 2287, 2297, 2311, 2339, 2341, 2393

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jul 16 2011

Keywords

• nonn

Examples

			433=1^3+3^3+4^3+5^3+6^3, 443=1^3+2^3+3^3+4^3+7^3, 541=1^3+2^3+4^3+5^3+7^3.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A122729, A193142, A193143.

Programs

Maple

N:= 3000: # for all terms <= N
S:= {}:
for a from 1 while 5*a^3 < N do
  for b from a+1 while a^3 + 4*b^3 < N do
    for c from b+1 while a^3 + b^3 + 3*c^3 < N do
      for d from c+1 while a^3 + b^3 + c^3 + 2*d^3 < N do
        S:= S union select(isprime,{seq(a^3 + b^3 + c^3 + d^3 + e^3, e=d+1..floor((N-a^3-b^3-c^3-d^3)^(1/3)))})
od od od od:
sort(convert(S,list)); # Robert Israel, Jun 21 2019

Mathematica

lst = {}; Do[Do[Do[Do[Do[p = a^3 + b^3 + c^3 + d^3 + e^3; If[PrimeQ[p], AppendTo[lst, p]], {e, d - 1, 1, -1}], {d, c - 1, 1, -1}], {c, b - 1, 1, -1}], {b, a - 1, 1, -1}], {a, 6, 20}]; Take[Union[lst], 80]
Module[{nn=15,upto},upto=nn^3+9;Select[Union[Total/@Subsets[Range[nn]^3,{5}]],PrimeQ[#] && #<=upto&]] (* Harvey P. Dale, Aug 31 2023 *)

PARI

cbrt(x)=if(x<0,x,x^(1/3));
upto(lim)=my(v=List(), tb, tc, td, te); for(a=6, lim^(1/3), for(b=4, min(a-1, cbrt(lim-a^2)), tb=a^3+b^3; for(c=3, min(b-1, cbrt(lim-tb)), tc=tb+c^3; for(d=2, min(c-1, cbrt(lim-tc)), td=tc+d^3; forstep(e=1+td%2, d-1, 2, te=td+e^3; if(te>lim, break); if(isprime(te), listput(v, te))))))); vecsort(Vec(v), , 8)
\\ Charles R Greathouse IV, Jul 17 2011