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 A235913 a(n) is the Manhattan distance between n^3 and (n+1)^3 in a square spiral of positive integers with 1 at the center. 0
 1, 3, 11, 15, 13, 9, 5, 21, 33, 59, 71, 49, 47, 35, 15, 13, 43, 73, 109, 123, 117, 109, 167, 141, 113, 77, 43, 5, 51, 95, 145, 201, 263, 281, 397, 413, 317, 333, 269, 239, 183, 121, 63, 11, 81, 147, 219, 307, 379, 471, 567, 623, 517, 569, 683, 503, 545, 473, 395, 311 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Spiral begins: .   49  26--27--28--29--30--31    |   |                   |   48  25  10--11--12--13  32    |   |   |           |   |   47  24   9   2---3  14  33    |   |   |   |   |   |   |   46  23   8   1   4  15  34    |   |   |       |   |   |   45  22   7---6---5  16  35    |   |               |   |   44  21--20--19--18--17  36    |                       |   43--42--41--40--39--38--37 LINKS EXAMPLE Manhattan distance between 2^3=8 and 3^3=27 is 3 in a square spiral, so a(2)=3. PROG (Python) import math def get_x_y(n):   sr = int(math.sqrt(n-1))  # Ok for small n's   sr = sr-1+(sr&1)   rm = n-sr*sr   d = (sr+1)/2   if rm<=sr+1:      return -d+rm, d   if rm<=sr*2+2:      return d, d-(rm-(sr+1))   if rm<=sr*3+3:      return d-(rm-(sr*2+2)), -d   return -d, -d+rm-(sr*3+3) for n in range(1, 77):   x0, y0 = get_x_y(n**3)   x1, y1 = get_x_y((n+1)**3)   print str(abs(x1-x0)+abs(y1-y0))+', ', CROSSREFS Cf. A214526, A232113, A232114, A232115. Sequence in context: A273869 A289049 A288980 * A132363 A134629 A245522 Adjacent sequences:  A235910 A235911 A235912 * A235914 A235915 A235916 KEYWORD nonn AUTHOR Alex Ratushnyak, Jan 16 2014 STATUS approved

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Last modified December 6 19:30 EST 2021. Contains 349567 sequences. (Running on oeis4.)