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%I #12 Jul 09 2023 12:19:41
%S -2,-6,-15,-42,143,136,23,-3135,1026,-2262,-25800,-26462,-954,-1417,
%T -608399,-34544,7656,-96222,13038,-34177,3825,2506,21505,-4959,
%U -25435062,-45457,-51958122,41838,-63855,-208464,55158,-7959246,-573242,-81840,154583,112014,183538,-931177,-2016462,-118026495,147345,-285769,553720,-568920,-5957082,-249102,550776,-1005577
%N Integer solutions to n^4 = x^3 + y^2 (values of x sorted by n).
%H Dario Alpern, <a href="https://www.alpertron.com.ar/SPOW432.HTM">List of first 1602 solutions to a^4 + b^3 = c^2 for increasing values of a</a>
%e 143 is in the sequence since we have 42^4 = 143^3 + 433^2.
%t (* 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]]
%Y Cf. A096741 for n-values and A221745 for y-values
%K sign
%O 1,1
%A _Jean-François Alcover_, Jan 24 2013
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