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 1-6 of 6 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
...

Links

Crossrefs

A087310 contains the corresponding common differences, A087308 the initial terms, A087309 the final terms.
Cf. A087308, A087309, A087310, A114660, A114663, A114670.
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

A087308 Initial terms associated with the arithmetic progressions in A086786.

Original entry on oeis.org

1, 2, 3, 5, 5, 7, 481, 635, 635, 199, 3841, 3841, 4979, 2995, 13561, 22903, 1691, 5951, 72697, 72697, 72697, 172151, 172151, 1782371, 1782371
Offset: 1

Views

Author

Amarnath Murthy, Sep 02 2003

Keywords

Links

Crossrefs

Cf. A086786, A087306, A087307, A087309, A087310.
Cf. A114664, A114671.

Extensions

More terms from David Wasserman, Jan 08 2006

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

Cf. A086786, A087308, A087309.

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.
Cf. A087309, A096003, A113470, A087308, A090547, A090549.

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

A113459 Least number that begins an arithmetic progression of n numbers with the same prime signature.

Original entry on oeis.org

1, 2, 3, 5, 5, 7, 7, 11, 11, 11, 11, 13
Offset: 1

Views

Author

David Wasserman, Jan 08 2006

Keywords

Comments

Initial terms of arithmetic progressions described in A113460. - N. J. A. Sloane, Oct 18 2007
Conjecture: For n > 1, a(n) = A007918(n). - David Wasserman, Jan 08 2006
I disagree with that conjecture! Ignoring the initial terms, this will agree with A007918 up to some point and then (presumably) drop below A007918. The initial term in the arithmetic progression (of length n) must be >= n, but it is likely to be less than A007918(n) if n is large. - N. J. A. Sloane, Oct 18 2007

Links

Crossrefs

Cf. A005115, A007918, A087309, A113460.
Cf. A113461, A127781, A007917, A061558.

Extensions

Edited by N. J. A. Sloane, Jul 01 2008 at the suggestion of R. J. Mathar.

A113462 Least number that ends an arithmetic progression of n numbers with distinct prime signatures.

Original entry on oeis.org

1, 2, 6, 8, 12, 28, 30, 180, 512, 720, 1648, 2300, 2416, 6084, 6160, 77688, 105408, 353736, 852912
Offset: 1

Views

Author

David Wasserman, Jan 08 2006

Keywords

Comments

Main diagonal of A113463.

Crossrefs

Cf. A087309, A113463.
Showing 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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