A104620 - OEIS

A104620

Consider the presentation of the digits of the natural numbers in a triangular form for successive bases, b. Now examine the main diagonal of these triangles and note the first occurrence of the n digits (0 through b-1). This is its own triangle presented here.

%I #7 Apr 23 2019 09:18:45

%S 1,2,1,4,1,9,6,1,8,2,3,1,4,2,19,10,1,7,2,5,31,8,1,6,2,10,18,3,14,1,7,

%T 2,11,12,3,10,4,1,29,2,8,13,3,12,62,13,1,5,2,12,6,3,9,23,73,12,1,9,2,

%U 13,11,3,16,7,80,4,22,1,8,2,6,15,3,18,19,10,4,37,11,1,9,2,13,70,3,7,26,16

%N Consider the presentation of the digits of the natural numbers in a triangular form for successive bases, b. Now examine the main diagonal of these triangles and note the first occurrence of the n digits (0 through b-1). This is its own triangle presented here.

%C See A104606 through A104613, A091425, A104614 through A104619 as examples in the OEIS data base for triangular forms to base n>1.

%C t(n,2)=1, t(n,4)=2, t(n,7)=3, t(n,11)=4, t(n,16)=5 and t(n,1+i(i+1)/2)=i.

%e Triangle begins:

%e 1

%e 2 1

%e 4 1 9

%e 6 1 8 2

%e 3 1 4 2 19

%e 10 1 7 2 5 31

%t f[n_] := If[n == 1, 0, Block[{t = Flatten[ IntegerDigits[ Range[ 2000], n]]}, u = t[[ Table[ i(i + 1)/2, {i, 100}]]]; Table[ Position[u, i, 1, 1], {i, 0, n - 1}]]]; Flatten[ Table[ f[n], {n, 13}]]

%Y Cf. A104606, A104607, A104608, A104609, A104610, A104611, A104612, A104613, A091425, A104614, A104615, A104616, A104617, A104618, A104619.

%K base,nonn,tabl

%O 1,2

%A _Robert G. Wilson v_, Mar 17 2005