The numbers were generated by an exhaustive search via a C-program.
FORMULA
Conjecture (by J. Fricke and G. Woeginger): The sequence contains all numbers n with an odd prime divisor p fullfilling n/p>2.
EXAMPLE
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.
