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 1-7 of 7 results.

A086786 Triangle read by rows: n-th row is the smallest set of n numbers in arithmetic progression with the same prime signature.

Original entry on oeis.org

1, 2, 3, 3, 5, 7, 5, 11, 17, 23, 5, 11, 17, 23, 29, 7, 37, 67, 97, 127, 157, 481, 485, 489, 493, 497, 501, 505, 635, 707, 779, 851, 923, 995, 1067, 1139, 635, 707, 779, 851, 923, 995, 1067, 1139, 1211, 199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089, 3841
Offset: 1

Views

Author

Amarnath Murthy, Sep 02 2003

Keywords

Comments

In this sequence "smallest" means that the last term of the arithmetic progression is minimized. A113460 minimizes the first term.

Examples

			Triangle begins:
1
2,3
3,5,7
5,11,17,23
5,11,17,23,29
7,37,67,97,127,157
481,485,489,493,497,501,505
635,707,779,851,923,995,1067,1139
635,707,779,851,923,995,1067,1139,1211
199,409,619,829,1039,1249,1459,1669,1879,2089
...
		

Crossrefs

A087310 contains the corresponding common differences, A087308 the initial terms, A087309 the final terms.
Row 10 is the same for A113470, A133276, A133277 and listed as A033168.

Extensions

Edited and extended by David Wasserman, Jan 08 2006
Further edits by N. J. A. Sloane, Oct 17 2007

A087309 Least number that ends an arithmetic progression of n numbers with the same prime signature.

Original entry on oeis.org

1, 3, 7, 23, 29, 157, 505, 1139, 1211, 2089, 5161, 5293, 6347, 10717, 14233, 28213, 31451, 72965, 119029, 121603, 124177, 611261, 632171, 2003171, 2012771
Offset: 1

Views

Author

Amarnath Murthy, Sep 02 2003

Keywords

Comments

Final terms of the arithmetic progressions described in A086786.
Main diagonal of A086786.

Crossrefs

Formula

a(n)=A087308(n)+(n-1)*A087310(n). - R. J. Mathar, Oct 19 2007

Extensions

Edited and extended by David Wasserman, Jan 08 2006
Further edited by N. J. A. Sloane, Jun 30 2008 at the suggestion of R. J. Mathar.

A090547 Leading entries in triangle in A090548 and A113470.

Original entry on oeis.org

1, 2, 3, 5, 5, 7, 35, 635, 635, 199, 3841, 3841, 4979, 2995, 13561, 22903, 1691, 5951, 72697, 72697, 72697, 172151, 172151, 1782371, 1782371
Offset: 1

Views

Author

Amarnath Murthy, Dec 09 2003

Keywords

Comments

Different from A087308.
In case there was more than one solution with minimum A090548(n), the one with minimum stride A090549(n) was selected to generate A090547(n) and A090549(n). - R. J. Mathar, Apr 28 2007

Crossrefs

Formula

A090548(n)=a(n)+(n-1)*A090549(n). - R. J. Mathar, Apr 28 2007

Extensions

Corrected and extended by R. J. Mathar, Apr 28 2007
More terms from David Wasserman, Jan 08 2006, May 11 2007
Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 11 2007

A090549 Common difference of arithmetic progression in n-th row of A090548 and A113470.

Original entry on oeis.org

1, 1, 2, 6, 6, 30, 30, 72, 72, 210, 132, 132, 114, 594, 48
Offset: 1

Views

Author

Amarnath Murthy, Dec 09 2003

Keywords

Comments

In case there was more than one solution with minimum A090548(n), the one with minimum stride A090549(n) was selected to generate A090547(n) and A090549(n). - R. J. Mathar, Apr 28 2007

Crossrefs

Formula

A090548(n)=A090547(n)+(n-1)*a(n). - R. J. Mathar, Apr 28 2007

Extensions

Corrected and extended by R. J. Mathar, Apr 28 2007

A087310 Common differences of arithmetic progressions in A086786.

Original entry on oeis.org

1, 2, 6, 6, 30, 4, 72, 72, 210, 132, 132, 114, 594, 48, 354, 1860, 3942, 2574, 2574, 2574, 20910, 20910, 9600, 9600
Offset: 2

Views

Author

Amarnath Murthy, Sep 02 2003

Keywords

Crossrefs

Formula

a(n) = A086786(n, 2) - A086786(n, 1) = (A087309(n) - A087308(n))/(n - 1).

Extensions

Edited and extended by David Wasserman, Jan 08 2006

A090548 Least number that ends an arithmetic progression of n numbers with the same number of divisors.

Original entry on oeis.org

1, 3, 7, 23, 29, 157, 215, 1139, 1211, 2089, 5161, 5293, 6347, 10717, 14233, 28213, 31451, 72965, 119029, 121603, 124177, 611261, 632171, 2003171, 2012771
Offset: 1

Views

Author

Amarnath Murthy, Dec 09 2003

Keywords

Comments

In the following triangle the n-th row contains the least set of n numbers in arithmetic progression with the same number of divisors. By "least" we mean that the largest term is minimized. Sequence contains the leading diagonal. In other words, largest of n numbers in arithmetic progression with the same tau function, or 0 if no such number exists.

Examples

			Triangle (A113470) begins:
1
2 3
3 5 7
5 11 17 23
5 11 17 23 29 ...
		

Crossrefs

Leading diagonal of A113470.

Formula

a(n)=A090547(n)+(n-1)*A090549(n). - R. J. Mathar, Apr 28 2007

Extensions

Corrected and extended by R. J. Mathar, Apr 28 2007
More terms from David Wasserman, Jan 08 2006, May 11 2007
Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 11 2007

A113464 First column of triangle A113463.

Original entry on oeis.org

1, 1, 2, 2, 8, 23, 24, 103, 304, 324, 8, 1024, 1024, 5096, 5096, 37548, 83520, 171360, 530424
Offset: 1

Views

Author

David Wasserman, Jan 08 2006

Keywords

Crossrefs

Showing 1-7 of 7 results.