

A153677


Minimal exponents m such that the fractional part of (1024/1000)^m obtains a minimum (when starting with m=1).


12



1, 68, 142, 341, 395, 490, 585, 1164, 1707, 26366, 41358, 46074, 120805, 147332, 184259, 205661, 385710, 522271, 3418770, 3675376, 9424094
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OFFSET

1,2


COMMENTS

Recursive definition: a(1)=1, a(n) is the least positive integer m such that the fractional part of (1024/1000)^m is less than the fractional part of (1024/1000)^k for all k, 1 <= k < m.


LINKS



FORMULA

Recursion: a(1):=1, a(k):=min{ m>1  fract((1024/1000)^m) < fract((1024/1000)^a(k1))}, where fract(x) = xfloor(x).


EXAMPLE

a(2)=68, since fract((1024/1000)^68) = 0.016456..., but fract((1024/1000)^k) >= 0.024 for 1 <= k <= 67; thus fract((1024/1000)^68) < fract((1024/1000)^k) for 1 <= k < 68.


MATHEMATICA

$MaxExtraPrecision = 10000;
p = .999;
Select[Range[1, 50000],
If[FractionalPart[(1024/1000)^#] < p,
p = FractionalPart[(1024/1000)^#]; True] &] (* Robert Price, Mar 15 2019 *)


PROG

(PARI) upto(n) = my(res = List(), r = 1, p = 1); for(i=1, n, c = frac(p *= 1.024); if(c<r, r=c; print1(i", "); listput(res, i))); res \\ David A. Corneth, Mar 15 2019


CROSSREFS



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



