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 A304586 A linear mapping a(n) = x + d*n of pairs of integers (x,d), where the pairs are enumerated by the counterclockwise square spiral (an axis-parallel number spiral) starting at 0. 7
 0, 1, 3, 3, 3, -1, -7, -7, -7, -7, 2, 13, 26, 27, 28, 29, 30, 15, -2, -21, -42, -43, -44, -45, -46, -47, -23, 3, 31, 61, 93, 95, 97, 99, 101, 103, 105, 71, 35, -3, -43, -85, -129, -131, -133, -135, -137, -139, -141, -143, -96, -47, 4, 57, 112, 169, 228, 231, 234, 237, 240, 243 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The sequence is a solution to the riddle described in the comments of A304584 without the restriction of x and d to nonnegative numbers. LINKS Rainer Rosenthal, Table of n, a(n) for n = 0..10000 EXAMPLE This is the standard counterclockwise square spiral starting at 0. - N. J. A. Sloane, Oct 17 2019 d: 3 | 36--35--34--33--32--31--30 55 | | | | 2 | 37 16--15--14--13--12 29 54 | | | | | | 1 | 38 17 4---3---2 11 28 53 | | | | | | | | 0 | 39 18 5 0---1 10 27 52 | | | | | | | -1 | 40 19 6---7---8---9 26 51 | | | | | -2 | 41 20--21--22--23--24--25 50 | | | -3 | 42--43--44--45--46--47--48--49 _________________________________ x: -3 -2 -1 0 1 2 3 4 . a(9) = 2 + 9*(-1) = -7 because the 9th position in the spiral corresponds to x = 2 and d = -1, a(14) = 0 + 14*2 = 28 because the 14th position in the spiral corresponds to x = 0 and d = 2, a(25) = 3 + 25*(-2) = -47 because the 25th position in the spiral corresponds to x = 3 and d = -2. MAPLE square2pair:=proc(sq)local w, k; w:=floor(sqrt(sq)); k:=floor(w/2); if modp(sq, 2)=0 then return[-k, k]; else return[k+1, -k]; fi; end:pos2pS:=proc(n)local w, q, Q, e, E, sp; w:=floor(sqrt(n)); q := w^2; Q:=(w+1)^2; e:=n-q; E:=Q-n; if e

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Last modified December 6 20:19 EST 2023. Contains 367614 sequences. (Running on oeis4.)