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A367619 a(n) is the most remote positive ancestor of n in the comma-child graph in base 3.

%I A367619 #14 Feb 07 2024 13:21:43
%S A367619 1,2,3,3,1,1,7,1,2,2,7,1,1,2,1,1,1,1,7,1,1,2,1,7,1,7,1,1,1,1,1,1,7,7,
%T A367619 1,1,1,7,1,1,1,1,1,1,7,7,1,1,1,7,1,1,1,1,1,1,1,7,1,1,1,1,7,1,7,1,1,1,
%U A367619 1,1,1,1,7,1,1,1,1,7,1,7,1,1,1,1,1,1,7
%N A367619 a(n) is the most remote positive ancestor of n in the comma-child graph in base 3.
%C A367619 Analogous to A367617, but the calculations are done in base 3.
%C A367619 See A367338 for definitions of comma-child.
%C A367619 The sequence consists entirely of terms in {1, 2, 3, 7}.  In particular, two terms, a(3) = a(4) = 3; five terms, a(2,9,10,14,22) = 2; and 490 terms are 7, ending with a(2182). All other terms a(k) are 1, since a(2183..2190) = 1 and 1 <= p(n) - n <= b^2 - 1 (= 8 for base b = 3).
%H A367619 Michael S. Branicky, <a href="/A367619/b367619.txt">Table of n, a(n) for n = 1..2200</a>
%H A367619 Eric Angelini, Michael S. Branicky, Giovanni Resta, N. J. A. Sloane, and David W. Wilson, The Comma Sequence: A Simple Sequence With Bizarre Properties, <a href="http://arxiv.org/abs/2401.14346">arXiv:2401.14346</a>, <a href="https://www.youtube.com/watch?v=_EHAdf6izPI">Youtube</a>
%F A367619 a(n) is defined as n if A367618(n) = -1, else A367618(A367618(n)).
%o A367619 (Python)
%o A367619 from functools import cache
%o A367619 from sympy.ntheory.factor_ import digits
%o A367619 def comma_parent(n, base=3): # A367618(n)
%o A367619     y = digits(n, base)[1]
%o A367619     x = (n-y)%base
%o A367619     k = n - y - base*x
%o A367619     return k if k > 0 else -1
%o A367619 @cache
%o A367619 def a(n):
%o A367619     cp = comma_parent(n)
%o A367619     if cp <= 0: return n
%o A367619     return a(cp)
%o A367619 print([a(n) for n in range(1, 88)])
%Y A367619 Cf. A367338, A367355, A367617, A367618.
%K A367619 nonn,base
%O A367619 1,2
%A A367619 _Michael S. Branicky_ and _N. J. A. Sloane_, Dec 20 2023