A198445 Values y of record minima of the positive distance d between the square of an integer y and the fifth power of a positive integer x such that d = y^2 - x^5 (x <> k^2 and y <> k^5).

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

Offset

1,1

Comments

Distance d is equal to 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), the distance d between the square of an integer y and the 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: A014070 A320287 A365776 * A248377 A326968 A209497

Adjacent sequences: A198442 A198443 A198444 * A198446 A198447 A198448

Keyword

nonn

Author

Artur Jasinski, Oct 25 2011

Status

approved