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A179791 Values x for records of minima of positive distance d between a ninth power of positive integer x and a square of integer y such d = x^9 - y^2 (x<>k^2 and y<>k^9). 12
2, 3, 5, 6, 8, 13, 22, 23, 27, 62, 78, 147, 181, 203, 233, 468, 892, 1110, 1827, 3657, 3723, 10637, 11145, 11478, 12275, 16764, 19151, 22719, 23580, 24974, 30163, 36885, 41759, 41948, 44427, 66443, 86167, 96658, 115992, 222962, 248461, 248588, 384573 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Distance d is equal 0 when x = k^2 and y = k^9.

For d values see A179790.

For y values see A179792.

Conjecture (Artur Jasinski):

For any positive number x >= A179791(n) distance d between ninth power of x and square of any y (such that x<>k^2 and y<>k^9) can't be less than A179790(n).

LINKS

Table of n, a(n) for n=1..43.

MATHEMATICA

d = 9; 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}]; xx (* Artur Jasinski *)

CROSSREFS

Cf. A179107, A179108, A179109, A179386, A179387, A179388, A179407, A179408, A179784, A179785, A179786, A179790, A179791, A179792, A179793, A179794, A179795.

Sequence in context: A144712 A050028 A239135 * A139443 A239263 A216293

Adjacent sequences:  A179788 A179789 A179790 * A179792 A179793 A179794

KEYWORD

nonn

AUTHOR

Artur Jasinski, Jul 27 2010

STATUS

approved

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Last modified August 3 22:03 EDT 2021. Contains 346441 sequences. (Running on oeis4.)