cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 16 results. Next

A137752 First numerator and then denominator (left to right) of Leibniz's harmonic-like triangle.

Original entry on oeis.org

1, 1, 1, 2, 1, 2, 1, 3, 5, 6, 1, 3, 1, 4, 7, 12, 7, 12, 1, 4, 1, 5, 9, 20, 31, 30, 9, 20, 1, 5, 1, 6, 11, 30, 49, 60, 49, 60, 11, 30, 1, 6, 1, 7, 13, 42, 71, 105, 209, 140, 71, 105, 13, 42, 1, 7, 1, 8, 15, 56, 97, 168, 351, 280, 351, 280, 97, 168
Offset: 1

Views

Author

Mohammad K. Azarian, Feb 10 2008

Keywords

Comments

In this triangle the right-hand edge consists of the reciprocals of the positive integers. A number that is not in this edge is obtained by adding the number diagonally above it to the number to its immediate right. Note that in Leibniz's harmonic triangle we subtract the two numbers to get a number which is not on the right-hand edge.

Examples

			1/1;
1/2, 1/2;
1/3, 5/6, 1/3;
1/4, 7/12, 7/12, 1/4;
1/5, 9/20, 31/30, 9/20, 1/5;

Crossrefs

Cf. A003506; A007622; A046201; A046204; A046205; A046206; A046208; A046212.
Cf. A137753

A137753 First denominator and then numerator (left to right) of Leibniz's harmonic-like triangle.

Original entry on oeis.org

1, 1, 2, 1, 2, 1, 3, 1, 6, 5, 3, 1, 4, 1, 12, 7, 12, 7, 4, 1, 5, 1, 20, 9, 30, 31, 20, 9, 5, 1, 6, 1, 30, 11, 60, 49, 60, 49, 30, 11, 6, 1, 7, 1, 42, 13, 105, 71, 140, 209, 105, 71, 42, 13, 7, 1, 8, 1, 56, 15, 168, 97, 280, 351, 280, 351, 168, 97
Offset: 1

Views

Author

Mohammad K. Azarian, Feb 10 2008

Keywords

Examples

			1/1; --> 1 1
1/2, 1/2; --> 2 1 2 1
1/3, 5/6, 1/3; --> 3 1 6 5 3 1
1/4, 7/12, 7/12, 1/4; --> 4 1 12 7 12 7 4 1
1/5, 9/20, 31/30, 9/20, 1/5; --> 5 1 20 9 30 31 20 9 5 1

Crossrefs

Cf. A003506; A007622; A046201; A046204; A046205; A046206; A046208; A046212; A137752.
Cf. A137752

A137754 Numerators (left to right) of Leibniz's harmonic-like triangle.

Original entry on oeis.org

1, 1, 1, 1, 5, 1, 1, 7, 7, 1, 1, 9, 31, 9, 1, 1, 11, 49, 49, 11, 1, 1, 13, 71, 209, 71, 13, 1, 1, 15, 97, 351, 351, 97, 15, 1, 1, 17, 127, 545, 1471, 545, 127, 17, 1, 1, 19, 161, 799, 2561, 2561, 799, 161, 19, 1, 1, 21, 199, 1121, 4159, 10625, 4159, 1121, 199, 21, 1
Offset: 1

Views

Author

Mohammad K. Azarian, Feb 10 2008

Keywords

Examples

			1/1; --> 1
1/2, 1/2; --> 1 1
1/3, 5/6, 1/3; --> 1 5 1
1/4, 7/12, 7/12, 1/4; --> ...
1/5, 9/20, 31/30, 9/20, 1/5;

Crossrefs

Cf. A137752.
Cf. A003506; A007622; A046201; A046204; A046205; A046206; A046208; A046212; A137753.

A137755 Nontrivial numerators (left to right) of Leibniz's harmonic-like triangle.

Original entry on oeis.org

5, 7, 7, 9, 31, 9, 11, 49, 49, 11, 13, 71, 209, 71, 13, 15, 97, 351, 351, 97, 15, 17, 127, 545, 1471, 545, 127, 17, 19, 161, 799, 2561, 2561, 799, 161, 19, 21, 199, 1121, 4159, 10625, 4159, 1121, 199, 21
Offset: 1

Views

Author

Mohammad K. Azarian, Feb 10 2008

Keywords

Examples

			1/1; -->
1/2, 1/2;  -->
1/3, 5/6, 1/3; --> 5
1/4, 7/12, 7/12, 1/4; --> 7 7
1/5, 9/20, 31/30, 9/20, 1/5; --> 9 31 9

Crossrefs

Cf. A003506; A007622; A046201; A046204; A046205; A046206; A046208; A046212; A137752; A137753; A137754.

A137756 Nontrivial elements in writing the numerator of an element first and then the denominator of that element (left to right) of Leibniz's harmonic-like triangle. That is, the nontrivial elements of A137752.

Original entry on oeis.org

2, 2, 3, 5, 6, 3, 4, 7, 12, 7, 12, 4, 5, 9, 20, 31, 30, 9, 20, 5, 6, 11, 30, 49, 60, 49, 60, 11, 30, 6, 7, 13, 42, 71, 105, 209, 140, 71, 105, 13, 42, 7, 8, 15, 56, 97, 168, 351, 280, 351, 280, 97, 168, 15, 56, 8, 9, 17, 72, 127, 252, 545, 504, 1471
Offset: 1

Views

Author

Mohammad K. Azarian, Feb 10 2008

Keywords

Examples

			1/1; -->
1/2, 1/2; --> 2 2
1/3, 5/6, 1/3; --> 3 5 6 3
1/4, 7/12, 7/12, 1/4; --> ...
1/5, 9/20, 31/30, 9/20, 1/5;

Crossrefs

Cf. A003506; A007622; A046201; A046204; A046205; A046206; A046208; A046212; A137752; A137753; A137754; A137755.

A137757 Nontrivial elements in writing the denominator of an element first and then the numerator of that element (left to right) of Leibniz's harmonic-like triangle. That is, the nontrivial elements of A137753.

Original entry on oeis.org

2, 2, 3, 6, 5, 3, 4, 12, 7, 12, 7, 4, 5, 20, 9, 30, 31, 20, 9, 5, 6, 30, 11, 60, 49, 60, 49, 30, 11, 6, 7, 42, 13, 105, 71, 140, 209, 105, 71, 42, 13, 7, 8, 56, 15, 168, 97, 280, 351, 280, 351, 168, 97, 56, 15, 8, 9, 72, 17, 252, 127, 504, 545, 630, 1471
Offset: 1

Views

Author

Mohammad K. Azarian, Feb 10 2008

Keywords

Examples

			1/1; -->
1/2, 1/2; --> 2 2
1/3, 5/6, 1/3; --> 3 6 5 3
1/4, 7/12, 7/12, 1/4; --> ...
1/5, 9/20, 31/30, 9/20, 1/5;

Crossrefs

Cf. A003506; A007622; A046201; A046204; A046205; A046206; A046208; A046212; A137752; A137753; A137754; A137755; A137756.

A137758 Odd elements in writing the denominator of an element first and then the numerator of that element (left to right) of Leibniz's harmonic-like triangle. That is, the odd elements of A137753.

Original entry on oeis.org

1, 1, 1, 1, 3, 1, 5, 3, 1, 1, 7, 7, 1, 5, 1, 9, 31, 9, 5, 1, 1, 11, 49, 49, 11, 1, 7, 1, 13, 105, 71, 209, 105, 71, 13, 7, 1, 1, 15, 97, 351, 351, 97, 15, 1, 9, 1, 17, 127, 545, 1471, 545, 127, 17, 9, 1, 1, 19, 161, 799, 2561, 2561, 799, 161, 19, 1
Offset: 1

Views

Author

Mohammad K. Azarian, Feb 10 2008

Keywords

Examples

			1/1; --> 1 1
1/2, 1/2; --> 1 1
1/3, 5/6, 1/3; --> 3 1 5 3 1
1/4, 7/12, 7/12, 1/4; --> ...
1/5, 9/20, 31/30, 9/20, 1/5;

Crossrefs

Cf. A003506; A007622; A046201; A046204; A046205; A046206; A046208; A046212; A137752; A137753; A137754; A137755; A137756; A137757.

A137759 Odd numbers in writing first numerator and then denominator (left to right) of Leibniz's harmonic-like triangle.

Original entry on oeis.org

1, 1, 1, 1, 1, 3, 5, 1, 3, 1, 7, 7, 1, 1, 5, 9, 31, 9, 1, 5, 1, 11, 49, 49, 11, 1, 1, 7, 13, 71, 105, 209, 71, 105, 13, 1, 7, 1, 15, 97, 351, 351, 97, 15, 1, 1, 9, 17, 127, 545, 1471, 545, 127, 17, 1, 9, 1, 19, 161, 799, 2561, 2561, 799, 161, 19, 1
Offset: 1

Views

Author

Mohammad K. Azarian, Feb 11 2008

Keywords

Examples

			1/1; --> 1 1
1/2, 1/2; --> 1 1
1/3, 5/6, 1/3; --> 1 3 5 1 3
1/4, 7/12, 7/12, 1/4; -->
1/5, 9/20, 31/30, 9/20, 1/5;

Crossrefs

Cf. A003506, A007622, A046201, A046204, A046205, A046206, A046208, A046212, A137752, A137753, A137754, A137755, A137756, A137757, A137758.

A137760 Distinct numbers in writing first numerator and then denominator (left to right) of Leibniz's harmonic-like triangle.

Original entry on oeis.org

1, 2, 3, 5, 6, 4, 7, 12, 9, 20, 31, 30, 11, 49, 60, 13, 42, 71, 105, 209, 140, 8, 15, 56, 97, 168, 351, 280, 17, 72, 127, 252, 545, 504, 1471, 630, 10, 19, 90, 161, 360, 799, 840, 2561, 1260, 21, 110, 199, 495, 1121, 1320, 4159, 2310, 10625, 2772
Offset: 1

Views

Author

Mohammad K. Azarian, Feb 11 2008

Keywords

Examples

			1/1; --> 1
1/2, 1/2; --> 2
1/3, 5/6, 1/3; --> 3 5 6
1/4, 7/12, 7/12, 1/4; --> ...
1/5, 9/20, 31/30, 9/20, 1/5;

Crossrefs

Cf. A046201; A046204; A046205; A046206; A046208; A046212; A137752; A137753; A137754; A137755; A137756; A137757; A137758; A137759.

A137761 Distinct numbers in writing first denominator and then numerator (left to right) of Leibniz's harmonic-like triangle.

Original entry on oeis.org

1, 2, 3, 6, 5, 4, 12, 7, 20, 9, 30, 31, 11, 60, 49, 42, 13, 105, 71, 140, 209, 8, 56, 15, 168, 97, 280, 351, 72, 17, 252, 127, 504, 545, 630, 1471, 10, 90, 19, 360, 161, 840, 799, 1260, 2561, 110, 21, 495, 199, 1320, 1121, 2310, 4159, 2772, 10625
Offset: 1

Views

Author

Mohammad K. Azarian, Feb 11 2008

Keywords

Examples

			1/1; --> 1
1/2, 1/2;  --> 2
1/3, 5/6, 1/3;  --> 3 6 5
1/4, 7/12, 7/12, 1/4;
1/5, 9/20, 31/30, 9/20, 1/5;

Crossrefs

Cf. A046201; A046204; A046205; A046206; A046208; A046212; A137752; A137753; A137754; A137755; A137756; A137757; A137758; A137759, A137760.
Showing 1-10 of 16 results. Next

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