A351832 Least nonnegative integer m such that n = x^6 + y^6 - (z^2 + m^2) for some nonnegative integers x,y,z with z <= m.

0, 0, 0, 6, 6, 20, 7, 7, 19, 24, 24, 7, 6, 6, 5, 5, 7, 26, 26, 6, 6, 22, 9, 5, 5, 6, 98, 6, 6, 6, 5, 5, 4, 4, 32, 5, 5, 26, 5, 4, 4, 20, 322, 7, 4, 4, 3, 3, 4, 4, 22, 3, 3, 22, 3, 3, 2, 2, 418, 2, 2, 2, 1, 1, 0, 0, 94, 6, 23, 20, 7, 19, 24, 20, 20, 7, 6, 22, 5, 7, 19, 18, 18, 6, 22, 37, 59, 5, 6, 24, 24, 6, 6, 21

Offset: 0

Author

Zhi-Wei Sun, Feb 21 2022

Keywords

• nonn

Comments

Conjecture: a(n) exists for each nonnegative integer n.

See also Conjecture 2 in A351341.

Examples

			a(170) = 2730 with 170 = 9^6 + 15^6 - (2114^2 + 2730^2).
a(5938) = 16184 with 5938 = 17^6 + 25^6 - (2520^2 + 16184^2).
a(9746) = 7600 with 9746 = 11^6 + 21^6 - (5456^2 + 7600^2).
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000290, A001014, A001481, A351321, A351338, A351341, A351375, A351376.

Programs

Mathematica

QQ[n_]:=IntegerQ[n^(1/6)];
tab={};Do[m=0; Label[bb]; k=m^2; Do[If[QQ[n+k+x^2-y^6], tab=Append[tab,m];Goto[aa]],  {x, 0, m}, {y, 0, ((n+k+x^2)/2)^(1/6)}];m=m+1; Goto[bb]; Label[aa], {n, 0, 100}];Print[tab]