A351376 Least nonnegative integer m such that n = x^3 + y^3 - (z^5 + m^5) for some nonnegative integers x,y,z with z <= m.

0, 0, 0, 2, 76, 3, 1, 1, 0, 0, 6, 5, 4, 7, 1, 1, 0, 51, 129, 14, 22, 2, 2, 4, 136, 1, 1, 0, 0, 27, 7, 2, 2, 1, 1, 0, 3, 3, 14, 2, 2, 44, 11, 5, 8, 6, 101, 4, 4, 28, 14, 6, 1, 1, 0, 17, 42, 33, 2, 2, 20, 2, 1, 1, 0, 0, 3, 8, 3, 2, 1, 1, 0, 3, 6, 41, 3, 43, 12, 10, 10, 6, 6, 6, 59, 29, 33, 81, 2, 1, 1, 0, 2, 2, 2, 2, 2, 3, 3, 3, 2

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

Cf. A000578, A000584, A004842, A004999, A351338, A351341, A351375.

Sequence in context: A091978 A282966 A351433 * A276203 A324216 A198704

Adjacent sequences: A351373 A351374 A351375 * A351377 A351378 A351379

Keyword

nonn

Author

Zhi-Wei Sun, Feb 09 2022

Status

approved