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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 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.)