

A308834


a(n) is the smallest error in trying to solve n^4 = x^4 + y^4. That is, for each n from 2 on, find positive integers x and y, x <= y < n such that n^4  x^4  y^4 is minimal and let a(n) = n^4  x^4  y^4.


1



14, 49, 94, 113, 46, 191, 399, 64, 657, 545, 466, 721, 145, 1328, 270, 2751, 719, 751, 1118, 1376, 1041, 1839, 1310, 1663, 815, 5184, 306, 9104, 863, 1455, 4320, 7024, 5105, 4289, 11504, 64, 12016, 2816, 10799, 11200, 6094, 2671, 226, 20753
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

2,1


COMMENTS

This sequence was suggested to me by Moshe Shmuel Newman.
This is A135998 with the exponent 4 replacing 3.


LINKS

Table of n, a(n) for n=2..45.


EXAMPLE

Here are the calculations for the first few values.
For 2, the only possible values for x and y are 1,1, so we have
a(2) = 2^4  1^4  1^4 = 16  2 = 14.
For 3, y can be 1 or 2. if y is 1, x is 1 as well, and if y=2, then x can be 1 or 2.
3^4  1^4  1^4 = 79
3^4  1^4  2^4 = 64
3^4  2^4  2^4 = 49.
The smallest absolute value is in the last case, so a(3) = 49.


MATHEMATICA

nend = 100; For[n = 2, n <= nend, n++, a[n] = 0]; For[n = 2, n <= nend, n++, min = n^4; For[y = 1, y <= n  1, y++, For [x = y, x <= n  1, x++, changed = False; sol = n^4  x^4  y^4; If[(sol < min) && (sol > 0), min = sol; changed = True]; If[(Abs[sol] < min) && (sol < 0), min = sol; changed = True]; If[changed, a[n] = sol]]]]; Print[t = Table[a[i], {i, 2, nend}]] (* or *)
a[n_] := SortBy[n^4  Flatten[Table[x^4 + y^4, {x, n1}, {y, x}]], Abs][[1]]; Array[a, 99, 2] (* Giovanni Resta, Jul 05 2019 *)


CROSSREFS

Cf. A135998.
Sequence in context: A039340 A043163 A043943 * A084049 A251221 A302467
Adjacent sequences: A308831 A308832 A308833 * A308835 A308836 A308837


KEYWORD

sign


AUTHOR

David S. Newman, Jun 27 2019


STATUS

approved



