%I #6 Oct 29 2023 17:28:16
%S 9,12,15,18,20,21,24,25,27,28,30,33
%N Numbers of children for which there is a subset which cannot be generated by a counting-out game.
%C The numbers were generated by an exhaustive search via a C-program.
%F Conjecture (by J. Fricke and G. Woeginger): The sequence contains all numbers n with an odd prime divisor p satisfying n/p>2.
%e For 9 children 1,2,3,4,5,6,7,8,9, there is no possibility to select 3,4,6,7 (in any order) by a counting-out game, e.g. for selecting 3,4,6,7 the count-to number has to be 3 mod 9, 1 mod 8, 2 mod 7 and 1 mod 6, which is impossible.
%Y Complement of A119485.
%K nonn,more
%O 1,1
%A _Jan Fricke_, May 23 2006