The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A351341 Least nonnegative integer m such that n = x^4 + y^4 - (z^3 + m^3) for some nonnegative integers x,y,z with z <= m. 4
 0, 0, 0, 63, 3, 3, 4, 2, 2, 2, 4, 21, 37, 6, 1, 1, 0, 0, 4, 11, 7, 14, 5, 2, 2, 4, 8, 3, 3, 5, 1, 1, 0, 4, 4, 45, 5, 5, 11, 6, 6, 6, 32, 3, 7, 11, 3, 3, 6, 8, 8, 48, 13, 3, 3, 3, 6, 6, 31, 20, 93, 55, 3, 49, 33, 2, 2, 5, 5, 3, 3, 4, 2, 2, 2, 69, 17, 29, 11, 1, 1, 0, 0, 5, 61, 29, 8, 5, 2, 2, 4, 21, 29, 51, 6, 1, 1, 0, 4, 85, 13 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Conjecture 1: Let k be 4 or 5. Then each integer can be written as x^k + y^k - (z^3 + w^3) with x,y,z,w nonnegative integers. Two examples for k = 5: -4 = 58^5 + 76^5 - (775^3 + 1397^3) and 14 = 40^5 + 67^5 - (125^3 + 1132^3). Conjecture 2: Let k be among 4, 5, 6 and 7. Then any integer can be written as x^k + y^k - (z^2 + w^2) with x,y,z,w nonnegative integers. Examples for k = 6, 7: 170 = 9^6 + 15^6 - (2114^2 + 2730^2) and 469 = 7^7 + 8^7 - (1001^2 + 1385^2). Conjecture 3: For any integer k > 3, there are no nonnegative integers x,y,z,w such that x^k + y^k - (z^k + w^k) = 3. See also another similar conjecture in A351338. LINKS Zhi-Wei Sun, Table of n, a(n) for n = 0..10000 EXAMPLE a(60) = 93 with 60 = 25^4 + 27^4 - (49^3 + 93^3). a(527) = 527 with 527 = 29^4 + 110^4 - (91^3 + 527^3). a(2198) = 1704 with 2198 = 85^4 + 304^4 - (1539^3 + 1704^3). a(4843) = 1965 with 4843 = 142^4 + 338^4 - (1804^3 + 1965^3). MATHEMATICA QQ[n_]:=IntegerQ[n^(1/4)]; tab={}; Do[m=0; Label[bb]; k=m^3; Do[If[QQ[n+k+x^3-y^4], tab=Append[tab, m]; Goto[aa]], {x, 0, m}, {y, 0, ((n+k+x^3)/2)^(1/4)}]; m=m+1; Goto[bb]; Label[aa], {n, 0, 100}]; Print[tab] CROSSREFS Cf. A000578, A000583, A000584, A001014, A001015, A001481, A004831, A004999, A351306, A351321, A351338. Sequence in context: A324018 A102241 A255915 * A234692 A339458 A084507 Adjacent sequences:  A351338 A351339 A351340 * A351342 A351343 A351344 KEYWORD nonn AUTHOR Zhi-Wei Sun, Feb 08 2022 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 8 14:52 EDT 2022. Contains 356009 sequences. (Running on oeis4.)