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

%I #19 Dec 25 2023 12:21:46

%S -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,10,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,20,11,

%T 2,-1,-1,-1,-1,-1,-1,-1,-1,30,21,12,3,-1,-1,-1,-1,-1,-1,-1,40,31,22,

%U 13,4,-1,-1,-1,-1,-1,-1,50,41,32,23,14,14,5,-1,-1,-1,-1,60,51,42,33,33,24,15,6,-1,-1,-1,70,61,52,52,43,34,25,16,7

%N a(n) is the unique k such that n is a comma-child of k, or -1 if k does not exist.

%C Similar to A367614, but here we give the k such that n is a comma-child of k, whereas in A367614 n has to be a comma-successor of k. See A367338 for definitions.

%C The first difference between A367614 and the present sequence arises because 14 has one comma-successor, 59, but has two comma-children, 59 and 60. So A367614(59) = 14, A367614(60) = -1, while in the present sequence we have a(59) = a(60) = 14.

%C There are similar differences at n = 69 and 70, because both are comma-children of 33, and at many other places.

%H Michael S. Branicky, <a href="/A367616/b367616.txt">Table of n, a(n) for n = 1..10000</a>

%o (Python)

%o def a(n):

%o y = int(str(n)[0])

%o x = (n-y)%10

%o k = n - y - 10*x

%o return k if k > 0 else -1

%o print([a(n) for n in range(1, 86)]) # _Michael S. Branicky_, Dec 18 2023

%Y Cf. A121805, A367338, A367346, A367614.

%K sign,base

%O 1,11

%A _N. J. A. Sloane_, Dec 18 2023