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
Keywords
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
Programs
-
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)))