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A221745 Integer solutions to n^4 = x^3 + y^2 (values of y sorted by n). 1
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Jan 24 2013

STATUS

approved

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Last modified September 15 18:47 EDT 2019. Contains 327083 sequences. (Running on oeis4.)