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%I #10 Jul 09 2023 12:19:36
%S 3,29,76,397,433,4785,6083,175784,32507,143027,4146689,4308693,298483,
%T 648613,474554340,7079295,3085855,30042907,3881837,8288063,5692856,
%U 5734653,7790076,8893220,128277120493,22015007,374524445203,49060477,54142096,109233295,63051523,22454830331,444716637,101907569,105952427,169483859,169792053,949475843,2882277973,1282239885136,353814916,395856397,100314399,655054991,14549866883,579133627,433336175,1177246693
%N Integer solutions to n^4 = x^3 + y^2 (values of y 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 433 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, 3]]
%Y Cf. A096741 for n-values and A221744 for x-values
%K nonn
%O 1,1
%A _Jean-François Alcover_, Jan 24 2013
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