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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.
1
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
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
Sequence in context: A249569 A094500 A049473 * A095769 A080820 A356989
KEYWORD
nonn
AUTHOR
David Fifield, Jan 17 2009
STATUS
approved