A092363 n^(1/a(n)) is the closest to an integer on 2..n with a(n) minimal.

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?

Links

Table of n, a(n) for n=2..97.

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

Adjacent sequences: A092360 A092361 A092362 * A092364 A092365 A092366

Keyword

nonn

Author

Jon Perry, Mar 19 2004

Status

approved