A154951 Found by taking the tree defined by the Hofstadter H-sequence (A005374), mirroring it left to right and relabeling the nodes so they increase left to right. a(n) is the parent node of node n in the tree so constructed.

0, 1, 1, 2, 3, 4, 4, 5, 6, 6, 7, 8, 9, 9, 10, 10, 11, 12, 13, 13, 14, 15, 15, 16, 16, 17, 18, 19, 19, 20, 21, 22, 22, 23, 24, 24, 25, 25, 26, 27, 28, 28, 29, 29, 30, 31, 32, 32, 33, 34, 35, 35, 36, 37, 37, 38, 38, 39, 40, 41, 41, 42, 43, 43, 44, 44, 45, 46, 47, 47

Offset

0,4

References

D. R. Hofstadter, Goedel, Escher, Bach: an Eternal Golden Braid, Basic Books, 1999, p. 137.

Links

David Fifield Table of n, a(n) for n = 0..10000

Prog

(Python) # Emulate a breadth-first traversal of the "flip"
# of the tree defined by the Hofstadter H-sequence.
def hflip_iter():
    yield 0
    yield 1
    # Start on the first node of a left branch, parent node is 1.
    queue = [(1, 1)]
    n = 2
    while True:
        parent, state = queue.pop(0)
        yield parent
        if state == 0:
            # Root node. Add the two children.
            queue.append((n, 1))
            queue.append((n, 0))
        elif state == 1:
            # First node on left branch. Add the second node.
            queue.append((n, 2))
        elif state == 2:
            # Second node on left branch. Add a new root.
            queue.append((n, 0))
        n += 1
i = hflip_iter()
for n in range(0, 10001):
    print("%d %d" % (n, next(i)))

Crossrefs

Cf. A005374, A123070.

Sequence in context: A249569 A094500 A049473 * A095769 A080820 A356989

Adjacent sequences: A154948 A154949 A154950 * A154952 A154953 A154954

Keyword

nonn

Author

David Fifield, Jan 17 2009

Status

approved