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
Keywords
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
Programs
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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
Comments