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A179794 Values x for records of minima of positive distance d between a eleventh power of positive integer x and a square of integer y such d = x^11 - y^2 (x<>k^2 and y<>k^11) 12
2, 3, 6, 7, 8, 10, 14, 18, 20, 26, 28, 32, 38, 52, 60, 77, 145, 168, 222, 237, 268, 279, 286, 359, 367, 390, 536, 569, 622, 872, 1085, 1349, 1462, 1760, 1932, 2423, 2801, 5559, 5925, 7052, 8383, 8752, 10075, 11917, 15712, 17420, 17598, 23712, 26026, 28095 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Distance d is equal 0 when x = k^2 and y = k^11.

For x values see A179794.

For x values see A179795.

Conjecture (*Artur Jasinski*):

For any positive number x >= A179794(n) distance d between eleventh power of x

and square of any y (such that x<>k^2 and y<>k^11) can't be less than A179793(n).

LINKS

Table of n, a(n) for n=1..50.

MATHEMATICA

d = 11; 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: A028768 A294484 A064528 * A221977 A001162 A072685

Adjacent sequences:  A179791 A179792 A179793 * A179795 A179796 A179797

KEYWORD

nonn

AUTHOR

Artur Jasinski, Jul 27 2010

STATUS

approved

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Last modified June 21 00:01 EDT 2021. Contains 345317 sequences. (Running on oeis4.)