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A060467 Value of z 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, 1, 1, 1, 2, 2, 2, 2, 2, 3, -11, 2, 1626, 2, 3, 3, 3, 16, 15584139827, 3, 3, 3, 3, 3, 2220422932, 8866128975287528, 3, 3, 3, 4, 4, -159380 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

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) = 2220422932. A solution to A060464(25) = 33 remains to be found. Other values for larger n can be found in the last 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

Table of n, a(n) for n=0..31.

A. Bogomolny, Finicky Diophantine Equations on cut-the-knot.org, accessed Nov. 10, 2015

H. 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 1626.

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]; A060467 = Table[z /. ToRules[ Simplify[ r[A060464[[k]], A060465[[k]]] /. C[1] -> 0]], {k, 1, Length[A060464]}] (* Jean-François Alcover, Jul 11 2012 *)

CROSSREFS

Cf. A060464, A060465, A060466.

Sequence in context: A029116 A064770 A322073 * A125918 A239202 A083533

Adjacent sequences:  A060464 A060465 A060466 * A060468 A060469 A060470

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 15584139827, 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

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Last modified October 21 18:54 EDT 2019. Contains 328308 sequences. (Running on oeis4.)