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A179408 Values y for records of minima of positive distance d between a fifth power of a positive integer x and a square of an integer y such d = x^5 - y^2 (x != k^2 and y != k^5). 23
181, 22434, 50354, 2759646, 3834168, 5562261, 10980023, 18329057, 142674503, 2093555387, 12135618855, 29588700403, 72673092233, 423129175811, 425213412449, 2855547523353, 482836315990072, 484925830443335 (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^5.

For d values, see A179406.

For x values, see A179407.

Conjecture (from Artur Jasinski):

For any positive number x >= A179407(n), the distance d between fifth power of x and the square of any y (such that x != k^2 and y != k^5) can't be less than A179406(n).

LINKS

Table of n, a(n) for n=1..18.

J. Blass, A Note on Diophantine Equation Y^2 + k = X^5, Math. Comp. 1976, Vol. 30, No. 135, pp. 638-640.

A. Bremner, On the Equation Y^2 = X^5 + k, Experimental Mathematics 2008 Vol. 17, No. 3, pp. 371-374.

FORMULA

A179407(n)^5-a(n)^2 = A179406(n).

MATHEMATICA

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^5)^(1/2)]; k = n^5 - 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, 96001}]; dd = {}; xx = {}; yy = {}; Do[AppendTo[dd, vecd[[n]]]; AppendTo[xx, vecx[[n]]]; AppendTo[yy, vecy[[n]]], {n, 1, len}]; yy (* Artur Jasinski, Jul 13 2010 *)

CROSSREFS

Cf. A179107, A179108, A179109, A179386, A179387, A179388, A179406, A179407.

Sequence in context: A070250 A226714 A083979 * A224991 A189342 A189778

Adjacent sequences:  A179405 A179406 A179407 * A179409 A179410 A179411

KEYWORD

nonn,uned

AUTHOR

Artur Jasinski, Jul 13 2010

STATUS

approved

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Last modified May 28 21:37 EDT 2020. Contains 334690 sequences. (Running on oeis4.)