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 A193141 Primes that are the sum of 5 distinct positive cubes. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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] 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

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Last modified May 30 02:25 EDT 2023. Contains 363044 sequences. (Running on oeis4.)