A179786 Values y for records of the minima of the positive distance d between the seventh power of a positive integer x and the square of an integer y such that d = x^7 - y^2 (x <> k^2 and y <> k^7).

11, 46, 529, 1448, 3162, 10267, 24743, 35777, 116159, 147885, 370447, 1233870, 1577546, 6392774, 211053546, 264783325, 272123427, 1011697339, 1140219273, 2370360092, 49411058753, 63606986977, 71996746561757, 137783827309893

Offset

1,1

Comments

Distance d is equal to 0 when x = k^2 and y = k^7.

For d values see A179784.

For x values see A179785.

Conjecture (Artur Jasinski): For any positive number x >= A179785(n), the distance d between the seventh power of x and the square of any y (such that x <> k^2 and y <> k^7) can't be less than A179784(n).

Links

Table of n, a(n) for n=1..24.

Mathematica

d = 7; 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

Crossrefs

Cf. A179107, A179108, A179109, A179386, A179387, A179388, A179407, A179408, A179784, A179785.

Sequence in context: A177370 A126672 A361888 * A238584 A033209 A107216

Adjacent sequences: A179783 A179784 A179785 * A179787 A179788 A179789

Keyword

nonn

Author

Artur Jasinski, Jul 27 2010

Status

approved