This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A060466 Value of y 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, 1, 1, -1, -1, 0, 1, 1, -2, 10, 2, -1609, 2, -2, -2, -2, -14, -15550555555, -1, -1, 0, 1, 1, -2218888517, -8778405442862239, 2, 2, 2, -3, -3, 134476 (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) = -2218888517. A solution to A060464(25) = 33 remains to be found. Other values for larger n can be found in the second 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, Section D5. LINKS A. Bogomolny, Finicky Diophantine Equations on cut-the-knot.org, accessed Nov. 10, 2015 A.-S. Elsenhans, J. Jahnel, New sums of three cubes, Math. Comp. 78 (2009) 1227-1230 K. Koyama, Y. Tsuruoka, H. Sekigawa, On searching for solutions of the Diophantine equation x^3+y^3+z^3=n, Math. Comp. 66 (1997) 841 Eric S. Rowland, Known families of integer solutions of x^3+y^3+z^3=n Hisanori Mishima, About n=x^3+y^3+z^3 A. Tyszka, A hypothetical upper bound for the solutions of a Diophantine equation with a finite number of solutions, arXiv:0901.2093 [math.NT], 2009-2014. EXAMPLE For n=16 the smallest solution is 16 = (-511)^3 + (-1609)^3 + 1626^3, which gives the term -1609. MATHEMATICA nmax = 29; A060464 = Select[Range[0, nmax], Mod[#, 9] != 4 && Mod[#, 9] != 5 &]; A060465 = {0, 0, 0, 1, -1, 0, 0, 0, 1, -2, 7, -1, -511, 1, -1, 0, 1, -11, -2901096694, -1, 0, 0, 0, 1}; r[n_, x_] := Reduce[0 <= Abs[x] <= Abs[y] <= Abs[z] && n == x^3 + y^3 + z^3, {y, z}, Integers]; A060466 = Table[y /. ToRules[ Simplify[ r[A060464[[k]], A060465[[k]]] /. C -> 0]], {k, 1, Length[A060464]}] (* Jean-François Alcover, Jul 11 2012 *) CROSSREFS Cf. A060465, A060467, A173515. Sequence in context: A188635 A246479 A171659 * A243992 A317549 A239083 Adjacent sequences:  A060463 A060464 A060465 * A060467 A060468 A060469 KEYWORD sign,nice,hard,more AUTHOR N. J. A. Sloane, Apr 10 2001 EXTENSIONS In order to be consistent with A060465, where only primitive solutions are selected, a(18)=2 was replaced with -15550555555, by Jean-François Alcover, Jul 11 2012 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 October 21 20:44 EDT 2019. Contains 328315 sequences. (Running on oeis4.)