Voozh

A232115

a(n) is the Manhattan distance between n and n(n+1)/2 in a square spiral of positive integers with 1 at the center.

0, 1, 3, 4, 2, 3, 5, 6, 4, 5, 9, 6, 6, 7, 11, 8, 8, 15, 9, 10, 10, 13, 11, 12, 22, 11, 15, 18, 12, 15, 17, 22, 12, 21, 25, 10, 26, 21, 19, 18, 24, 27, 15, 34, 24, 21, 31, 20, 28, 21, 31, 24, 28, 41, 19, 36, 36, 23, 35, 26, 38, 23, 41, 36, 28, 53, 29, 38, 40, 31, 39

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

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

Numbers n such that a(n)*2=n: 2, 6, 10, 12, 14, 16, 20, 24, 30, 80, 192, 198, 350, 524, 536, 548, 552, 560, 564, 576, 588, 594, 606, 618, 630, 1380, 1900, 4446, ...

LINKS

Table of n, a(n) for n=1..71.

PROG

(Python)

import math

def get_x_y(n):

sr = math.isqrt(n-1)

sr = sr-1+(sr&1)

rm = n-sr*sr

d = (sr+1)//2

if rm<=sr+1:

return -d+rm, d