OFFSET
0,4
COMMENTS
Conjecture: a(n) exists for each nonnegative integer n.
See also Conjecture 2 in A351341.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 0..10000
EXAMPLE
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).
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]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Feb 21 2022
STATUS
approved