

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
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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 onetoone mapping from the nonnegative integers onto themselves.


REFERENCES



LINKS



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



KEYWORD

nonn


AUTHOR



STATUS

approved



