A241924 - OEIS

A241924

16*s^8 - 168*s^4*t^4 + 9*t^8, where s > 0, t = 1..s.

-143, 1417, -36608, 91377, -110448, -938223, 1005577, 362752, -2376023, -9371648, 6145009, 4572304, -2195951, -20040176, -55859375, 26656137, 23392512, 9296937, -28274688, -105690519, -240185088, 91833457, 85785232, 59623057, -10435568, -156352559

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Sequence lists, in nonincreasing order, the y-values in special solutions to x^4 + y^3 = z^2, that is: A241923(n)^4 + a(n)^3 = A241925(n)^2 (see also Cohen's post in Links section).

Note that 16*s^8 - 168*s^4*t^4 + 9*t^8 = (4*s^4 - 12*s^2*t^2 - 3*t^4)*(4s^4 + 12*s^2*t^2 - 3*t^4).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Dario Alpern, List of first 1602 solutions to a^4 + b^3 = c^2 for increasing values of a, where gcd(a,b,c) = 1.

Dario Alpern, Sum of powers, a^4 + b^3 = c^2.

Henri Cohen, a^m + b^n = c^p (was: Sum of two powers = Square), post in the newsgroup sci.math.research, Jan 09 1998.

MATHEMATICA

Flatten[Table[16 s^8 - 168 s^4 t^4 + 9 t^8, {s, 10}, {t, s}]]

PROG

(Magma) [16*s^8-168*s^4*t^4+9*t^8: t in [1..s], s in [1..10]];

CROSSREFS

Cf. A096741, A241923, A241925.