

A179800


Values y for records of minima of positive distance d between a thirteenth power of positive integer x and a square of integer y such d = x^13  y^2 (x<>k^2 and y<>k^13)


6



90, 1262, 34938, 114283, 741455, 5875603, 17403307, 28172943, 709955183, 936209559, 10875326100, 25905378592, 35572991418, 55703353220, 110485434560, 182204642678, 447245502234, 984322154617, 2160608565081, 3477146726351
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OFFSET

1,1


COMMENTS

Distance d is equal 0 when x = k^2 and y = k^13.
For d values see A179798.
For x values see A179799.
Conjecture (*Artur Jasinski*):
For any positive number x >= A179799(n) distance d between thirteenth power of x
and square of any y (such that x<>k^2 and y<>k^13) can't be less than A179798(n).


LINKS

Table of n, a(n) for n=1..20.


MATHEMATICA

d = 13; 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, A179798, A179799, A179800.
Sequence in context: A008449 A213455 A155016 * A133350 A279438 A250869
Adjacent sequences: A179797 A179798 A179799 * A179801 A179802 A179803


KEYWORD

nonn


AUTHOR

Artur Jasinski, Jul 27 2010


STATUS

approved



