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.

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, 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, 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

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Comments

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.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003015, A006987, A022911, A319382.

Programs

Maple

N:= 10000: # for binomial(n, k) values <= N
Res:= NULL:
for n from 2 while n*(n-1)/2 <= N do
  for k from 2 to n/2 do
    v:= binomial(n, k);
    if v > N then break fi;
    Res:= Res, [v, n, k]
od od:
Res:= sort([Res], proc(p, q) if p[1]<>q[1] then  p[1]q[2] then p[2]>q[2]
fi end proc): map(t -> t[3], Res); # Robert Israel, Sep 18 2018

Formula

A319382(n) = binomial(A022911(n),a(n)). - Robert Israel, Sep 18 2018

Extensions

Corrected by Robert Israel, Sep 18 2018