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.

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, 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, 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

Offset: 1

Author

Robert G. Wilson v, Mar 17 2005

Keywords

• base
• nonn
• tabl

Comments

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

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.

Examples

			Triangle begins:
1
2 1
4 1 9
6 1 8 2
3 1 4 2 19
10 1 7 2 5 31
		

Crossrefs

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

Programs

Mathematica

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}]]