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

1,1

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

Formula

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

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[1]
  elif p[2]<>q[2] then p[2]>q[2]
fi end proc): map(t -> t[3], Res); # Robert Israel, Sep 18 2018

Crossrefs

Cf. A003015, A006987, A022911, A319382.

Sequence in context: A359438 A279408 A135592 * A318955 A173883 A022922

Adjacent sequences: A022909 A022910 A022911 * A022913 A022914 A022915

Keyword

nonn

Author

Clark Kimberling

Extensions

Corrected by Robert Israel, Sep 18 2018

Status

approved