cp's OEIS Frontend

A022912 Arrange the nontrivial binomial coefficients C(m,k) (2 <= k <= m/2) in increasing order (not removing duplicates); record the sequence of k's.

%I A022912 #10 Sep 19 2018 02:57:30
%S A022912 2,2,2,3,2,2,3,2,2,2,3,2,4,2,3,2,2,2,3,4,2,2,3,2,2,2,4,3,2,5,2,2,3,2,
%T A022912 2,4,2,3,2,2,2,3,5,2,4,2,2,3,2,2,2,2,3,2,4,2,2,5,3,2,2,2,6,2,3,2,4,2,
%U A022912 2,2,3,2,2,2,5,2,3,4,2,2,2,2,3,2,2,2,6,2,3,4,2,2,2,5,2,3,2,2,2
%N A022912 Arrange the nontrivial binomial coefficients C(m,k) (2 <= k <= m/2) in increasing order (not removing duplicates); record the sequence of k's.
%C A022912 In case of duplicates, the k values are listed in increasing order.  Thus a(18)=2 and a(19)=3 corresponding to binomial(16,2)=binomial(10,3)=120.
%H A022912 Robert Israel, <a href="/A022912/b022912.txt">Table of n, a(n) for n = 1..10000</a>
%F A022912 A319382(n) = binomial(A022911(n),a(n)). - _Robert Israel_, Sep 18 2018
%p A022912 N:= 10000: # for binomial(n, k) values <= N
%p A022912 Res:= NULL:
%p A022912 for n from 2 while n*(n-1)/2 <= N do
%p A022912   for k from 2 to n/2 do
%p A022912     v:= binomial(n, k);
%p A022912     if v > N then break fi;
%p A022912     Res:= Res, [v, n, k]
%p A022912 od od:
%p A022912 Res:= sort([Res], proc(p, q) if p[1]<>q[1] then  p[1]<q[1]
%p A022912   elif p[2]<>q[2] then p[2]>q[2]
%p A022912 fi end proc): map(t -> t[3], Res); # _Robert Israel_, Sep 18 2018
%Y A022912 Cf. A003015, A006987, A022911, A319382.
%K A022912 nonn
%O A022912 1,1
%A A022912 _Clark Kimberling_
%E A022912 Corrected by _Robert Israel_, Sep 18 2018