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A303610 Circle aliasing numbers with 1/n size steps. 0
10, 1010, 110100, 11010100, 1101100100, 110110100100, 11101010101000, 1110110101001000, 111011010101001000, 11101101101001001000, 1110111010101010001000, 111011101010101010001000, 11110110110101010010010000, 1111011011010101010010010000, 111101110101101010010100010000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Starting from [-1,0] taking 2*n steps of length 1/n each either up or right, follow the path staying as close to the unit circle as possible. Every step up is considered a 1, every step right is considered a 0.

LINKS

Table of n, a(n) for n=1..15.

EXAMPLE

For n=3, we have 110100, meaning if we were to start at [-1, 0] and take 2*n=6 steps of length 1/n = 1/6 which can either be up or to the right, to follow the path of the unit circle the closest we would move up 1, up 1 again, then right, then up again, then right two more times, which we translate to the binary number 110100.

PROG

(Python)

def closer(pos1, pos2):

    dpos1 = (pos1[0]**2.0+pos1[1]**2.0)**.5

    dpos2 = (pos2[0]**2.0+pos2[1]**2.0)**.5

    if (1.0-dpos1)**2.0 < (1.0-dpos2)**2.0:

        return True

    else:

        return False

def converts(path):

    return ''.join(path)

l = []

for steps in range(1, 20):

    stepsize = 1.0/steps

    pos = [-1.0, 0.0]

    paths = []

    for i in range(0, 2*steps):

        if closer([pos[0]+stepsize, pos[1]], [pos[0], pos[1]+stepsize]):

            pos = [pos[0]+stepsize, pos[1]]

            paths.append(str(0))

        else:

            pos = [pos[0], pos[1]+stepsize]

            paths.append(str(1))

    l.append(int(converts(paths)))

print(l)

CROSSREFS

Subsequence of A035928 in binary.

Sequence in context: A163662 A176067 A080070 * A080120 A300571 A274069

Adjacent sequences:  A303607 A303608 A303609 * A303611 A303612 A303613

KEYWORD

nonn

AUTHOR

Ben Paul Thurston, May 06 2018

STATUS

approved

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Last modified July 31 05:49 EDT 2021. Contains 346367 sequences. (Running on oeis4.)