A367613 - OEIS

%I #21 Feb 07 2024 13:21:43

%S 1,2,3,4,5,6,7,8,9,10,11,12,13,15,16,17,19,20,21,22,23,24,25,26,28,29,

%T 30,31,32,34,35,37,38,39,40,41,42,43,44,46,47,48,49,50,51,53,55,56,57,

%U 58,59,60,61,62,64,65,66,67,68,69,70,73,74,75,76,77,78,79,80,82,83

%N Numbers with exactly one comma-child.

%C Complement of union of A367341 and A367346.

%C See A367338 for definition of comma-child.

%H Michael S. Branicky, <a href="/A367613/b367613.txt">Table of n, a(n) for n = 1..10000</a>

%H 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>

%t fQ[n_]:=Module[{k=n+10*Last[IntegerDigits[n]]+Range[9]},Length[Select[k,#-n==FromDigits[{Last[IntegerDigits[n]],First[IntegerDigits[#]]}]&]]]==1;

%t Select[Range[83],fQ[#]&] (* _Ivan N. Ianakiev_, Dec 16 2023 *)

%o (Python)

%o def ok(n):

%o     m = n + 10*(n%10)

%o     return len([m+y for y in range(1, 10) if int(str(m+y)[0]) == y]) == 1

%o print([k for k in range(1, 100) if ok(k)]) # _Michael S. Branicky_, Dec 28 2023

%Y Cf. A121895, A367341 (numbers with no comma-children), A367346 (numbers with two comma-children).

%K nonn,base

%O 1,2

%A _N. J. A. Sloane_, Dec 15 2023