

A130860


Number of decimal places of Pi given by integer approximations of the form a^(1/n).


0



0, 0, 2, 2, 4, 2, 3, 4, 5, 5, 6, 6, 6, 6, 9, 9, 9, 10, 10, 11, 11, 13, 12, 13, 13, 14, 14, 14
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


COMMENTS

Approximations are rounded, not truncated; see the example for n=2. Note that this can produce anomalous results; e.g., 0.148 does not match 0.152 to 1place accuracy, but does match it to 2place accuracy.  Franklin T. AdamsWatters, Mar 29 2014


LINKS

Table of n, a(n) for n=1..28.


FORMULA

a(n) = decimal_places in (round(Pi^n))^1/n w.r.t. Pi.
Note that round(Pi^n) is the sequence A002160 (Nearest integer to Pi^n).


EXAMPLE

a(8)=4 because 3.1416...= 9489^(1/8) is Pi accurate to 4 decimal places.
a(2)=0. 10^(1/2) = 3.16... rounded to one place is 3.2, while Pi to one place is 3.1.


PROG

(Python)
from math import pi, floor, ceil
def round(x):
return math.floor(x + 0.5)
def decimal_places(x, y):
dp = 1
# Compare integer part, shift 1 dp
while floor(x + 0.5) == floor(y + 0.5) and x and y:
x = (x  floor(x)) * 10
y = (y  floor(y)) * 10
dp = dp + 1
return dp
for n in range(1, 30):
pi_to_the_n = pow(pi, n)
pi_to_the_n_rnd = round(pi_to_the_n)
pi_approx = pow(pi_to_the_n_rnd, 1.0 / n)
dps = decimal_places(pi_approx, pi)
print(dps)


CROSSREFS

Cf. A002160.
Sequence in context: A103274 A046820 A043262 * A161535 A138785 A131817
Adjacent sequences: A130857 A130858 A130859 * A130861 A130862 A130863


KEYWORD

nonn,base,more


AUTHOR

Stephen McInerney (spmcinerney(AT)hotmail.com), Jul 22 2007


STATUS

approved



