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A179812 Record minima of the positive distance d between the fifteenth power of a positive integer x and the square of an integer y such that d = x^15 - y^2 (x <> k^2 and y <> k^15). 3
7, 7538, 283261, 494576, 4235622, 7135951, 38053824, 55905695, 185380312, 1208691743, 3263221507, 14034746735, 14732727599, 24211719874, 68491624661, 136264246246, 5337970328375, 6845918569200, 15505738619231, 30037885135088 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Distance d is equal to 0 when x = k^2 and y = k^15.
For x values see A179813.
For y values see A179814.
Conjecture: For any positive number x >= A179813(n), the distance d between the fifteenth power of x and the square of any y (such that x <> k^2 and y <> k^15) can't be less than A179812(n).
LINKS
MATHEMATICA
d = 15; max = 1000; vecd = Table[10^100, {n, 1, max}]; vecx = Table[10^100, {n, 1, max}]; vecy = Table[10^100, {n, 1, max}]; len = 1; Do[m = Floor[(n^d)^(1/2)]; k = n^d - m^2; If[k != 0, ile = 0; Do[If[vecd[[z]] < k, ile = ile + 1], {z, 1, len}]; len = ile + 1; vecd[[len]] = k; vecx[[len]] = n; vecy[[len]] = m], {n, 1, 10000000}]; dd = {}; xx = {}; yy = {}; Do[AppendTo[dd, vecd[[n]]]; AppendTo[xx, vecx[[n]]]; AppendTo[yy, vecy[[n]]], {n, 1, len}]; dd
CROSSREFS
Sequence in context: A220879 A119528 A116266 * A023344 A297050 A137693
KEYWORD
nonn
AUTHOR
Artur Jasinski, Jul 28 2010
STATUS
approved

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Last modified February 28 20:40 EST 2024. Contains 370400 sequences. (Running on oeis4.)