A104612 -id:A104612 - cp's OEIS frontend

A104615 Write the natural numbers in base 12 in a triangle with k digits in the k-th row, as shown below. Sequence gives the leading diagonal.

1, 3, 6, 10, 1, 4, 1, 2, 4, 9, 3, 3, 3, 10, 5, 6, 10, 7, 8, 9, 1, 0, 1, 1, 1, 1, 1, 3, 1, 1, 6, 1, 1, 8, 1, 1, 11, 2, 2, 3, 2, 2, 6, 2, 2, 10, 2, 3, 2, 3, 3, 6, 3, 3, 11, 4, 4, 3, 4, 4, 8, 4, 5, 2, 5, 5, 7, 5, 5, 1, 6, 6, 7, 6, 6, 1, 7, 7, 8, 7, 8, 2, 8, 8, 9, 9, 9, 5, 9, 9, 0, 10, 10, 8, 10, 11, 4, 11, 11, 0

Offset: 1

Robert G. Wilson v, Mar 16 2005

Cf. A104606, A104607, A104608, A104609, A104610, A104611, A104612, A104613, A091425, A104614, A104616, A104617, A104618, A104619, A104620.

t = Flatten[ IntegerDigits[ Range[1900], 12]]; t[[Table[n(n + 1)/2, {n, 100}]]]

A104616 Write the natural numbers in base 13 in a triangle with k digits in the k-th row, as shown below. Sequence gives the leading diagonal.

Original entry on oeis.org

1, 3, 6, 10, 1, 1, 7, 11, 2, 2, 0, 6, 4, 4, 1, 9, 6, 7, 10, 7, 9, 10, 1, 0, 1, 8, 4, 1, 10, 7, 1, 2, 0, 1, 10, 9, 1, 8, 8, 1, 9, 10, 2, 0, 2, 2, 7, 10, 2, 4, 8, 3, 4, 9, 3, 7, 0, 3, 0, 7, 4, 9, 4, 4, 8, 4, 4, 10, 7, 5, 2, 0, 5, 10, 9, 6, 8, 8, 6, 9, 10, 7, 0, 2, 7, 7, 10, 8, 4, 8, 8, 4, 9, 9, 7, 0, 9, 0, 7, 10

Offset: 1

Robert G. Wilson v, Mar 16 2005

1
23
456
789A
BC101
112131...

Cf. A104606, A104607, A104608, A104609, A104610, A104611, A104612, A104613, A091425, A104614, A104615, A104617, A104618, A104619, A104620.

t = Flatten[ IntegerDigits[ Range[1900], 13]]; t[[Table[n(n + 1)/2, {n, 100}]]]

A104617 Write the natural numbers in base 14 in a triangle with k digits in the k-th row, as shown below. Sequence gives the leading diagonal.

Original entry on oeis.org

1, 3, 6, 10, 0, 3, 1, 1, 1, 6, 2, 3, 10, 3, 4, 5, 13, 8, 7, 8, 10, 7, 10, 11, 1, 0, 1, 0, 1, 1, 2, 1, 1, 5, 1, 1, 7, 1, 1, 10, 1, 1, 13, 2, 2, 2, 2, 2, 6, 2, 2, 9, 2, 2, 13, 3, 3, 3, 3, 3, 8, 3, 3, 12, 4, 4, 3, 4, 4, 8, 4, 4, 13, 5, 5, 4, 5, 5, 10, 5, 6, 2, 6, 6, 8, 6, 6, 0, 7, 7, 6, 7, 7, 13, 8, 8, 6, 8, 8

Offset: 1

Robert G. Wilson v, Mar 16 2005

1
23
456
789A
BCD10
111213...

Cf. A104606, A104607, A104608, A104609, A104610, A104611, A104612, A104613, A091425, A104614, A104615, A104616, A104618, A104619, A104620.

t = Flatten[ IntegerDigits[ Range[1900], 14]]; t[[Table[n(n + 1)/2, {n, 100}]]]

A104618 Write the natural numbers in base 15 in a triangle with k digits in the k-th row, as shown below. Sequence gives the leading diagonal.

Original entry on oeis.org

1, 3, 6, 10, 1, 1, 6, 10, 2, 2, 10, 1, 3, 4, 7, 0, 5, 6, 12, 7, 8, 8, 10, 7, 11, 12, 1, 0, 1, 1, 1, 1, 1, 3, 1, 1, 5, 1, 1, 8, 1, 1, 11, 1, 1, 14, 2, 2, 2, 2, 2, 5, 2, 2, 9, 2, 2, 13, 2, 3, 2, 3, 3, 6, 3, 3, 10, 3, 3, 0, 4, 4, 5, 4, 4, 10, 4, 4, 0, 5, 5, 5, 5, 5, 11, 5, 6, 2, 6, 6, 8, 6, 6, 14, 7, 7, 5, 7, 7

Offset: 1

Robert G. Wilson v, Mar 16 2005

1
23
456
789A
BCDE1
011121...

Cf. A104606, A104607, A104608, A104609, A104610, A104611, A104612, A104613, A091425, A104614, A104615, A104616, A104617, A104619, A104620.

t = Flatten[ IntegerDigits[ Range[1900], 15]]; t[[Table[n(n + 1)/2, {n, 100}]]]

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.

Original entry on oeis.org

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

Robert G. Wilson v, Mar 17 2005

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.

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

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

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}]]

cp's OEIS Frontend

A104615 Write the natural numbers in base 12 in a triangle with k digits in the k-th row, as shown below. Sequence gives the leading diagonal.

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A104616 Write the natural numbers in base 13 in a triangle with k digits in the k-th row, as shown below. Sequence gives the leading diagonal.

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A104617 Write the natural numbers in base 14 in a triangle with k digits in the k-th row, as shown below. Sequence gives the leading diagonal.

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A104618 Write the natural numbers in base 15 in a triangle with k digits in the k-th row, as shown below. Sequence gives the leading diagonal.

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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.

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