login
A092363
n^(1/a(n)) is the closest to an integer on 2..n with a(n) minimal.
0
2, 2, 2, 2, 3, 3, 3, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 2, 2, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 2, 5, 5, 5, 5, 41, 42, 43, 44, 45, 46, 47, 2, 2, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97
OFFSET
2,1
COMMENTS
The sequence is conjectured to tend to n, as n^(1/n)->1. Is the density of nonnegative entries 0?
EXAMPLE
5^(1/2)= 2.236067977499789696409173668
5^(1/3)= 1.709975946676696989353108872
5^(1/4)= 1.495348781221220541911898994
5^(1/5)= 1.379729661461214832390063464
5^(1/2) is closest to an integer, so a(5)=2.
PROG
(PARI) { for (i=2, 100, xj=1; xm=0.5; for (j=2, i, x=i^(1/j)*1.0; xf=x-floor(x); if (xf<xm, xm=xf; xj=j); if (1-xf<xm, xm=1-xf; xj=j)); print1(", "xj)) }
CROSSREFS
Sequence in context: A350399 A347648 A184320 * A133874 A053384 A321857
KEYWORD
nonn
AUTHOR
Jon Perry, Mar 19 2004
STATUS
approved