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A179795 Values y 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
45, 420, 19047, 44467, 92681, 316227, 2012353, 8016758, 14310835, 60583368, 91068707, 189812531, 488438379, 2741690265, 6023263700, 23751934582, 771834189385, 1734606819630, 8034176335637, 11511075516802, 22632960587688 (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..21.

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}]; yy (*Artur Jasinski*)

CROSSREFS

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

Sequence in context: A156719 A228059 A155015 * A036495 A325981 A053137

Adjacent sequences:  A179792 A179793 A179794 * A179796 A179797 A179798

KEYWORD

nonn

AUTHOR

Artur Jasinski, Jul 27 2010

STATUS

approved

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Last modified June 15 11:44 EDT 2021. Contains 345048 sequences. (Running on oeis4.)