A084252 - OEIS

A084252

A measure of how close r^n is to an integer where r is the real root of x^3-x-1, i.e.. r = (1/2 + sqrt(23/108))^(1/3) + (1/2 - sqrt(23/108))^(1/3) = 1.3247.... (Higher absolute value of a(n) means closer, negative means less than closest integer.)

3, -4, 3, 13, 13, 2, 6, 2, -2, -3, 21, 5, -3, 4, -10, -18, 7, -6, 10, -139, -16, 11, -14, 39, 54, -23, 23, -39, 3479, 53, -40, 52, -158, -165, 78, -81, 148, 2429, -177, 140, -191, 657, 517, -269, 289, -563, -3923, 595, -492, 702, -2833, -1645, 933, -1041, 2156, 9021, -2012, 1740, -2590, 12872, 5304, -3242, 3756

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..63.

FORMULA

a(n) = round(1/(r^n - round(r^n))).

EXAMPLE

a(4)=13 since r^4 = 3.0795956..., 1/(3.0795956...-round(3.0795956...)) = 1/0.0795956... = 12.5635... and round(12.5635...) = 13.

CROSSREFS

Cf. A056581, A060006.

Positive values when n is in A051016 and negative when n is in A051017.