A077266 - OEIS

%I #10 Sep 02 2020 23:24:16

%S 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,

%T 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,

%U 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

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

%F 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.

%e Rows start:

%e   1;

%e   0,1;

%e   2,0,1;

%e   1,0,0,1;

%e   1,1,0,0,1;

%e   0,0,0,0,0,1;

%e   3,0,1,0,0,0,1;

%e   2,2,0,0,0,0,0,1;

%e   etc.

%e 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.

%o (PARI) T(n, k) = #select(x->(x==0), digits(n, k));

%o row(n) = vector(n-1, k, T(n,k+1));

%o tabl(nn) = for (n=2, nn, print(row(n))); \\ _Michel Marcus_, Sep 02 2020

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

%K base,nonn,tabl

%O 2,4

%A _Henry Bottomley_, Nov 01 2002