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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 1-place accuracy, but does match it to 2-place accuracy. - Franklin T. Adams-Watters, 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

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Last modified July 27 12:09 EDT 2021. Contains 346305 sequences. (Running on oeis4.)