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A179800
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Values y for record minima of the positive distance d between the thirteenth power of a positive integer x and the square of an integer y such that d = x^13 - y^2 (x <> k^2 and y <> k^13).
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6
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90, 1262, 34938, 114283, 741455, 5875603, 17403307, 28172943, 709955183, 936209559, 10875326100, 25905378592, 35572991418, 55703353220, 110485434560, 182204642678, 447245502234, 984322154617, 2160608565081, 3477146726351
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OFFSET
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1,1
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COMMENTS
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Distance d is equal to 0 when x = k^2 and y = k^13.
Conjecture: For any positive number x >= A179799(n), the distance d between the 13th power of x and the square of any y (such that x <> k^2 and y <> k^13) can't be less than A179798(n).
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LINKS
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MATHEMATICA
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d = 13; 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}]; yy
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CROSSREFS
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Cf. A179107, A179108, A179109, A179386, A179387, A179388, A179407, A179408, A179784, A179785, A179786, A179790, A179791, A179792, A179793, A179794, A179795, A179798, A179799, A179800.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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