OFFSET

0,5

COMMENTS

A number is visible from the current number if, given that it has coordinates (x,y) relative to the current number, the greatest common divisor of |x| and |y| is 1.

The magnitude of the numbers grow surprisingly quickly, e.g., a(150) = -4346232663618226. The only known terms that equal zero are a(0) and a(11); it is unknown whether more exist or if all integers eventually appear.

EXAMPLE

The spiral begins:

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-5....15...-8....9.....1 553

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-7 2....1.....1 0 -307

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-10 1 0.....1 -1 309

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14 3...-1.....6... -2 -61

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-29...58...-78...101...-118...150

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a(6) = 3 as from square 6, at (-1,1) relative to the starting square, the numbers currently visible are 1 (at -1,0), 0 (at 0,0), 1 (at 0,1), and 1 (at 1,0). These four numbers sum to 3, so a(6) = 3 so that 3 + 3 = 6.

a(7) = -1 as from square 7, at (0,-1) relative to the starting square, the numbers currently visible are 3 (at -1,-1), 1 (at -1,0), 2 (at -1,1), 0 (at 0,0), 1 (at 1,1), and 1 (at 1,0). These six numbers sum to 8, so a(7) = -1 so that -1 + 8 = 7.

CROSSREFS

KEYWORD

sign

AUTHOR

Scott R. Shannon, Oct 23 2022

STATUS

approved