OFFSET
0,4
COMMENTS
Conjecture: a(n) exists for any nonnegative integer n.
See also Conjecture 1 in A351341.
LINKS
Chai Wah Wu, Table of n, a(n) for n = 0..10000 (terms 0..100 from Zhi-Wei Sun)
EXAMPLE
a(4) = 76 with 4 = 775^3 + 1397^3 - (58^5 + 76^5).
a(18) = 129 with 18 = 1693^3 + 3137^3 - (3^5 + 129^5).
a(24) = 136 with 24 = 2534^3 + 3116^3 - (0^5 + 136^5).
a(87) = 81 with 87 = 140^3 + 1658^3 - (64^5 + 81^5).
From Chai Wah Wu, Feb 21 2022 : (Start)
a(389) = 3883 with 389 = 590621^3 + 877987^3 - (612^5 + 3883^5).
a(4173) = 3978 with 4173 = 16112^3 + 1108958^3 - (3259^5 + 3978^5).
(End)
MATHEMATICA
CQ[n_]:=IntegerQ[n^(1/3)];
tab={}; Do[m=0; Label[bb]; k=m^5; Do[If[CQ[n+k+x^5-y^3], tab=Append[tab, m]; Goto[aa]], {x, 0, m}, {y, 0, ((n+k+x^5)/2)^(1/3)}]; m=m+1; Goto[bb]; Label[aa], {n, 0, 100}]; Print[tab]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Feb 09 2022
STATUS
approved