A221744 Integer solutions to n^4 = x^3 + y^2 (values of x sorted by n).

-2, -6, -15, -42, 143, 136, 23, -3135, 1026, -2262, -25800, -26462, -954, -1417, -608399, -34544, 7656, -96222, 13038, -34177, 3825, 2506, 21505, -4959, -25435062, -45457, -51958122, 41838, -63855, -208464, 55158, -7959246, -573242, -81840, 154583, 112014, 183538, -931177, -2016462, -118026495, 147345, -285769, 553720, -568920, -5957082, -249102, 550776, -1005577

Offset

1,1

Links

Table of n, a(n) for n=1..48.

Dario Alpern, List of first 1602 solutions to a^4 + b^3 = c^2 for increasing values of a

Example

143 is in the sequence since we have 42^4 = 143^3 + 433^2.

Mathematica

(* Same program as A096741 except the final selection : *) nmax = 25000; r[{n_, x_}] := (rn = Reduce[x != 0 && y > 0 && GCD[n, x, y] == 1 && n^4 == x^3 + y^2, y, Integers]; If[rn =!= False, {n, x, y} /. ToRules[rn], {0, 0, 0}]); tab = Table[ r@{a[k][s, t] // Abs, -b[k][s, t]}, {k, 1, 7}, {s, -5, 8}, {t, 0, 5}] // Flatten[#, 2] & // Select[#, 0 < #[[1]] < nmax &] & // Union; Select[tab, # != {0, 0, 0} &][[All, 2]]

Crossrefs

Cf. A096741 for n-values and A221745 for y-values

Sequence in context: A307308 A065178 A178936 * A338861 A340726 A303833

Adjacent sequences: A221741 A221742 A221743 * A221745 A221746 A221747

Keyword

sign

Author

Jean-François Alcover, Jan 24 2013

Status

approved