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 A308293 Lexicographically earliest sequence of positive terms such that a(1) = 1, a(2) = 2, and for any n > 0, (abs(a(n+2)-a(n)), abs(a(n+2)-a(n+1))) is unique. 1
 1, 2, 1, 1, 1, 2, 3, 1, 1, 3, 1, 4, 1, 1, 4, 5, 1, 1, 5, 1, 2, 4, 6, 1, 1, 6, 1, 4, 6, 2, 1, 6, 2, 7, 1, 1, 7, 1, 8, 1, 1, 8, 3, 1, 7, 8, 1, 2, 5, 8, 1, 9, 1, 1, 9, 3, 1, 8, 9, 1, 3, 6, 10, 1, 1, 10, 1, 5, 8, 2, 10, 1, 8, 10, 1, 11, 1, 1, 11, 4, 1, 9, 10, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This sequence shows chaotic behavior (see scatterplot in Links section). This behavior is determined by the choice of the two leading terms. The variant, say b, with b(1) = b(2) = 1, corresponds to the natural numbers interspersed with pairs of ones: 1,1,1, 2,1,1, 3,1,1, etc. (b(n) = abs(A157128(n))). LINKS Rémy Sigrist, Table of n, a(n) for n = 1..10000 Rémy Sigrist, Colored scatterplot of (abs(a(n+2)-a(n)), abs(a(n+2)-a(n+1))) for n = 1..32702782 (where the hue is function of n) Rémy Sigrist, C program for A308293 EXAMPLE The first terms, alongside (abs(a(n+2)-a(n)), abs(a(n+2)-a(n+1))), are:   n   a(n)  (abs(a(n+2)-a(n)),abs(a(n+2)-a(n+1)))   --  ----  -------------------------------------    1     1  (0,1)    2     2  (1,0)    3     1  (0,0)    4     1  (1,1)    5     1  (2,1)    6     2  (1,2)    7     3  (2,0)    8     1  (2,2)    9     1  (0,2)   10     3  (1,3)   11     1  (0,3)   12     4  (3,0)   13     1  (3,3)   14     1  (4,1)   15     4  (3,4) PROG (C) See Links section. CROSSREFS See A080427 for a simpler variant. Cf. A157128. Sequence in context: A331958 A319193 A097886 * A249298 A088863 A053283 Adjacent sequences:  A308290 A308291 A308292 * A308294 A308295 A308296 KEYWORD nonn AUTHOR Rémy Sigrist, May 19 2019 STATUS approved

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Last modified May 14 16:48 EDT 2021. Contains 343898 sequences. (Running on oeis4.)