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 A340944 List of X-coordinates of point moving along one of the arms of a counterclockwise square spiral with four arms; A340945 gives Y-coordinates. 3
 0, 1, 1, 1, 0, -1, -2, -3, -3, -3, -3, -3, -3, -3, -2, -1, 0, 1, 2, 3, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 LINKS Rémy Sigrist, Table of n, a(n) for n = 0..10101 Rémy Sigrist, PARI program for A340944 Index entries for sequences related to coordinates of 2D curves FORMULA a(n) = A340945(n) iff n belongs to A002939. a(n) = - A340945(n) iff n = 4*x^2 - 6*x + 2 for some x. a(n) = 0 iff n is an even square (A016742). a(n) = Re z where z = (r-s*i)*i^s with s = round(sqrt(n)) = A000194(n) and remainder r = n - s^2. - Kevin Ryde, May 24 2023 EXAMPLE The spiral starts as follows: +-----+-----+-----+-----+ |7 6 5 4 |3 . | | . + +-----+-----+ + + |8 | | |2 | | | | | | + + +-----+-----+ + |9 | | |0 1 | | | | | | . + + + +-----+-----+ . |10 | | . | | | . + + +-----+-----+-----+-----+ .11 . . - so a(0) = a(4) = 0, a(1) = a(2) = a(3) = 1, a(5) = -1, a(6) = -2, a(7) = a(8) = a(9) = a(10) = a(11) = -3. PROG (PARI) See Links section. (PARI) a(n) = my(r, s=sqrtint(n, &r)); if(r>s, s++; r-=2*s-1); real((r-s*I)*I^s); \\ Kevin Ryde, May 24 2023 CROSSREFS Cf. A000194, A002939, A016742, A340171, A340945. Sequence in context: A247656 A294081 A192454 * A270533 A344511 A244919 Adjacent sequences: A340941 A340942 A340943 * A340945 A340946 A340947 KEYWORD sign,easy,look AUTHOR Rémy Sigrist, Jan 30 2021 STATUS approved

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Last modified July 13 11:43 EDT 2024. Contains 374282 sequences. (Running on oeis4.)