A077266 Triangle of number of zeros when n is written in base k (2 <= k <= n).

1, 0, 1, 2, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 3, 0, 1, 0, 0, 0, 1, 2, 2, 0, 0, 0, 0, 0, 1, 2, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset

2,4

Links

Table of n, a(n) for n=2..106.

Formula

T(nk, k)=T(n, k)+1; T(nk+m, k)=T(n, k) if 0<m<k; T(k, k)=1; T(n, k)=0 if n/2<k<n or 0<n<k.

Example

Rows start:
  1;
  0,1;
  2,0,1;
  1,0,0,1;
  1,1,0,0,1;
  0,0,0,0,0,1;
  3,0,1,0,0,0,1;
  2,2,0,0,0,0,0,1;
  etc.
9 can be written in bases 2-9 as: 1001, 100, 21, 14, 13, 12, 11 and 10, in which case the numbers of zeros are 2,2,0,0,0,0,0,1.

Prog

(PARI) T(n, k) = #select(x->(x==0), digits(n, k));
row(n) = vector(n-1, k, T(n, k+1));
tabl(nn) = for (n=2, nn, print(row(n))); \\ Michel Marcus, Sep 02 2020

Crossrefs

Columns include A023416 and A077267. Row sums are A033093, row maxima are A062842, number of positive terms in each row are A077268.

Sequence in context: A325226 A376847 A261812 * A366794 A214302 A129561

Adjacent sequences: A077263 A077264 A077265 * A077267 A077268 A077269

Keyword

base,nonn,tabl

Author

Henry Bottomley, Nov 01 2002

Status

approved