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A198445 Values y for records of minima of positive distance d between a square of integer y and a fifth power of positive integer x such that d = y^2 - x^5 (x<>k^2 and y<>k^5) 2
2, 6, 56, 2537, 3788, 45531, 90298, 110302, 3120599, 3280601, 3878907, 12325663, 14055482, 14645977, 42923597, 45730778, 183164286, 185898039, 926295393, 2054642668, 44803437862, 44877249113, 104775699199, 104939539201, 414619915847, 17920089051165, 21146208937291, 52744869326263, 95361328242187, 9537353527343 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Distance d is equal 0 when x = k^2 and y = k^5.

For d values see A198443.

For x values see A198444.

Conjecture (*Artur Jasinski*):

For any positive number x >= A198444(n) distance d between a square of any y and a fifth power of x such that x<>k^2 and y<>k^5) can't be less than A198443(n)

LINKS

Table of n, a(n) for n=1..30.

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)] + 1; k = m^2 - n^5; 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, 100000000}]; dd = {}; xx = {}; yy = {}; Do[AppendTo[dd, vecd[[n]]]; AppendTo[xx, vecx[[n]]]; AppendTo[yy, vecy[[n]]], {n, 1, len}]; vecy

CROSSREFS

Cf. A179406, A179407, A179408, A198443, A198444.

Sequence in context: A167010 A014070 A320287 * A248377 A326968 A209497

Adjacent sequences:  A198442 A198443 A198444 * A198446 A198447 A198448

KEYWORD

nonn

AUTHOR

Artur Jasinski, Oct 25 2011

STATUS

approved

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Last modified August 3 08:21 EDT 2021. Contains 346435 sequences. (Running on oeis4.)