This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A060465 Value of x of the solution to x^3 + y^3 + z^3 = A060464(n) (numbers not 4 or 5 mod 9) with smallest |z| and smallest |y|, 0 <= |x| <= |y| <= |z|. 4
 0, 0, 0, 1, -1, 0, 0, 0, 1, -2, 7, -1, -511, 1, -1, 0, 1, -11, -2901096694, -1, 0, 0, 0, 1, -283059965, -2736111468807040, -1, 0, 1, 0, 1, 117367 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,10 COMMENTS Indexed by A060464. Only primitive solutions where gcd(x,y,z) does not divide n are considered. From the solution A060464(24) = 30 = -283059965^3 - 2218888517^3 + 2220422932^3 (smallest possible magnitudes according to A. Bogomolny), one has a(24) = -283059965. A solution to A060464(25) = 33 remains to be found. Other values for larger n can be found in the first column of the table on Hisanori Mishima's web page. - M. F. Hasler, Nov 10 2015 REFERENCES R. K. Guy, Unsolved Problems in Number Theory, 3rd ed., Springer, New York, 2004, Section D5, 231-234. LINKS D. J. Bernstein, Three cubes A. Bogomolny, Finicky Diophantine Equations on cut-the-knot.org, accessed Nov. 10, 2015 B. Conn, L. Vaserstein, On sums of three integral cubes, Contemp. Math 166 (1994) MR1284068 V. L. Gardiner, R. B. Lazarus, P. R. Stein, Solutions of the diophantine equation x^3+y^3=z^3-d, Math. Comp. 18 (1964) 408-413. D.R. Heath-Brown, W.M. Lioen and H.J.J. te Riele on Solving the Diophantine Equation x3 + y3 + z3 = k on a Vector Computer J. C. P. Miller, M. F. C. Woollett, Solutions of the Diophantine Equation x^3+y^3+z^3=k, J. Lond. Math. Soc. 30 (1) (1955) 101-110 Hisanori Mishima, About n=x^3+y^3+z^3 EXAMPLE For n=16 the smallest solution is 16 = (-511)^3 + (-1609)^3 + 1626^3, which gives the term -511. MATHEMATICA (* this program is not convenient for hard cases *) nmax = 29; xmin[_] = 0; xmax[_] = 20; xmin = 500; xmax = 600; xmin = 2901096600; xmax = 2901096700; r[n_, x_] := Reduce[0 <= Abs[x] <= Abs[y] <= Abs[z] && n == x^3 + y^3 + z^3, {y, z}, Integers]; r[n_ /; IntegerQ[n^(1/3)]] := {0, 0, n^(1/3)}; mySort = Sort[#1, Which[Abs[#1[]] <= Abs[#2[]], True, Abs[#1[]] == Abs[#2[]], If[Abs[#1[]] <= Abs[#2[]], True, False], True, False] & ] & ; rep := {x_, y_, z_} /; (x + y == 0 && x > 0) :> {-x, -y, z}; r[n_] := Reap[Do[ sp = r[n, x] /. C -> 1; If[sp =!= False, xyz = {x, y, z} /. {ToRules[sp]} /. rep; If[GCD @@ Flatten[{n, xyz}] == 1, Sow[xyz]]]; sn = r[n, -x] /. C -> 1; If[sn =!= False, xyz = {-x, y, z} /. {ToRules[sn]} /. rep; If[GCD @@ Flatten[{n, xyz}] == 1, Sow[xyz]]], {x, xmin[n], xmax[n]}]][[2, 1]] // Flatten[#, 1] & // mySort // First; A060464 = Select[Range[0, nmax], Mod[#, 9] != 4 && Mod[#, 9] != 5 &]; A060465 = Table[xyz = r[n]; Print[ " n = ", n, " {x, y, z} = ", xyz]; xyz[], {n, A060464}] (* Jean-François Alcover, Jul 10 2012 *) CROSSREFS Cf. A060466, A060467, A173515. Sequence in context: A248676 A125699 A242207 * A219177 A139339 A090986 Adjacent sequences:  A060462 A060463 A060464 * A060466 A060467 A060468 KEYWORD sign,nice,hard,more AUTHOR N. J. A. Sloane, Apr 10 2001 EXTENSIONS Edited and a(24) added by M. F. Hasler, Nov 10 2015 a(25) from Tim Browning and further terms added by Charlie Neder, Mar 09 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 23 02:37 EDT 2019. Contains 327327 sequences. (Running on oeis4.)