A367617 a(n) is the most remote positive ancestor of n in the comma-child graph.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 1, 13, 14, 15, 16, 17, 18, 19, 20, 21, 20, 10, 2, 25, 26, 27, 28, 29, 30, 31, 32, 30, 21, 1, 3, 37, 38, 39, 40, 41, 42, 43, 40, 31, 20, 13, 4, 49, 50, 51, 52, 53, 54, 50, 41, 32, 10, 14, 14, 5, 62, 63, 64, 65, 14, 51, 42, 30, 30, 2, 15, 6, 74, 75
Offset: 1
Examples
a(60) = a(66) = 14, since 66 is a comma-child of 60, and 60 is a comma-child of 14, and 14 is not the comma-child of any positive number. In other words, A367616(A367616(66)) = A367616(60) = 14, and A367616(14) = -1.
Links
- Michael S. Branicky, Table of n, a(n) for n = 1..10000
- Eric Angelini, Michael S. Branicky, Giovanni Resta, N. J. A. Sloane, and David W. Wilson, The Comma Sequence: A Simple Sequence With Bizarre Properties, arXiv:2401.14346, Youtube
Programs
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Python
def comma_parent(n): # A367616(n) y = int(str(n)[0]) x = (n-y)%10 k = n - y - 10*x return k if k > 0 else -1 def a(n): an = n while (cp:=comma_parent(an)) > 0: an = cp return an print([a(n) for n in range(1, 76)]) # Michael S. Branicky, Dec 18 2023
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