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A367618 a(n) is the unique k such that n is a comma-child of k in base 3, or -1 if k does not exist.

%I A367618 #17 Feb 07 2024 13:21:43
%S A367618 -1,-1,-1,3,1,1,-1,6,2,9,7,5,12,10,8,15,13,13,11,18,16,14,21,19,17,24,
%T A367618 20,27,25,23,30,28,26,33,31,29,36,34,32,39,37,35,42,40,38,45,43,41,48,
%U A367618 46,44,51,49,49,47,54,52,50,57,55,53,60,58,56,63,61,59,66,64,62,69,67,65,72,70,68,75,73,71,78,74,81,79,77,84,82
%N A367618 a(n) is the unique k such that n is a comma-child of k in base 3, or -1 if k does not exist.
%C A367618 Analogous to A367616, but the calculations are done in base 3.
%C A367618 See A367338 for definitions of comma-child.
%C A367618 May also be called the "comma-parent" of n since n is the comma-child of a(n).
%H A367618 Michael S. Branicky, <a href="/A367618/b367618.txt">Table of n, a(n) for n = 1..10000</a>
%H A367618 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 A367618 a(n) = n - y - b*((n-y) mod b) where b is the base and y is the first digit of a(n); it is said to exist if a(n) > 0, else undefined (here, -1).
%o A367618 (Python)
%o A367618 from functools import cache
%o A367618 from sympy.ntheory.factor_ import digits
%o A367618 def a(n, base=3):
%o A367618     y = digits(n, base)[1]
%o A367618     x = (n-y)%base
%o A367618     k = n - y - base*x
%o A367618     return k if k > 0 else -1
%o A367618 print([a(n) for n in range(1, 88)])
%Y A367618 Cf. A367338, A367355, A367616, A367619.
%K A367618 sign,base
%O A367618 1,4
%A A367618 _Michael S. Branicky_ and _N. J. A. Sloane_, Dec 20 2023