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

1,1

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A122729, A193142, A193143.

Sequence in context: A047804 A008691 A269881 * A360652 A051964 A142686

Adjacent sequences: A193138 A193139 A193140 * A193142 A193143 A193144

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jul 16 2011

Status

approved