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 A359008 Jane Street's infinite sidewalk's greedy walk inverse mapping. 6
 0, 1, 2, 5, 3, 6, 9, 4, 7, 15, 10, 29, 13, 8, 16, 27, 11, 30, 49, 14, 60, 25, 17, 28, 47, 12, 31, 58, 50, 23, 34, 61, 26, 45, 18, 64, 56, 48, 75, 21, 32, 59, 105, 51, 24, 70, 35, 62, 54, 81, 46, 73, 19, 65, 111, 57, 103, 214, 76, 22, 68, 33, 244, 87, 106, 52 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS For n a nonnegative integer, a(n) is the smallest nonnegative integer i such that A359005(i) == n. In fact, if a(n) exists, it is actually the unique nonnegative integer i such that A359005(i) == n. ({A359005(n)} is demonstrably an injective mapping from the nonnegative integers onto themselves.) It is conjectured that a(n) exists for all nonnegative n. This has been verified true with a computer for all n < 7884654. This would make {a(n)} a one-to-one mapping from the nonnegative integers onto themselves. REFERENCES Inverse mapping of A359005. LINKS Neal Gersh Tolunsky, Table of n, a(n) for n = 0..10000 PROG (Python) def a(n: int) -> int: if n < 0: raise Exception("n must be a nonnegative integer") i = 0 if n == 0: return i visited = {0} slab = 1 while True: i += 1 if slab == n: return i visited.add(slab) label = 1 + (slab >> 1) if not slab - label in visited: slab -= label # jumping backwards else: slab += label # jumping forwards if slab in visited: raise Exception(f"blocked at slab {slab}") CROSSREFS Cf. A358838, A359005. Sequence in context: A256997 A335499 A358838 * A239970 A111202 A194280 Adjacent sequences: A359005 A359006 A359007 * A359009 A359010 A359011 KEYWORD nonn AUTHOR Frederic Ruget, Dec 11 2022 STATUS approved

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Last modified August 15 19:07 EDT 2024. Contains 375173 sequences. (Running on oeis4.)