A221745 Integer solutions to n^4 = x^3 + y^2 (values of y sorted by n).

3, 29, 76, 397, 433, 4785, 6083, 175784, 32507, 143027, 4146689, 4308693, 298483, 648613, 474554340, 7079295, 3085855, 30042907, 3881837, 8288063, 5692856, 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

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

433 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, 3]]

Crossrefs

Cf. A096741 for n-values and A221744 for x-values

Sequence in context: A119951 A296246 A257293 * A087210 A288918 A190942

Adjacent sequences: A221742 A221743 A221744 * A221746 A221747 A221748

Keyword

nonn

Author

Jean-François Alcover, Jan 24 2013

Status

approved