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 1-5 of 5 results.

A113461 Common differences of arithmetic progressions in A113460.

Original entry on oeis.org

0, 1, 2, 6, 6, 30, 150, 1210230, 32671170, 224494620, 1536160080, 1482708889200
Offset: 1

Views

Author

David Wasserman, Jan 08 2006

Keywords

Comments

Apart from the initial term, does this sequence coincide with A061558? Does A113460 coincide with A130791? - N. J. A. Sloane, Sep 22 2007
Apart from the initial term, this sequence coincides with A061558 for at least the first 210 terms. - David W. Wilson, Sep 22 2007

Links

Crossrefs

Cf. A113460, A113459, A127781.

A127781 Last term of arithmetic progression of numbers with same prime signature described in A113460.

Original entry on oeis.org

1, 3, 7, 23, 29, 157, 907, 8471621, 261369371
Offset: 1

Views

Author

N. J. A. Sloane, Oct 17 2007

Keywords

Links

Crossrefs

Apart from leading term, agrees with A120302 for many terms. Where is the first difference?

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

A130791 Triangle read by rows: n-th row is the lexicographically earliest arithmetic progression of n primes beginning with A007918(n).

Original entry on oeis.org

2, 2, 3, 3, 5, 7, 5, 11, 17, 23, 5, 11, 17, 23, 29, 7, 37, 67, 97, 127, 157, 7, 157, 307, 457, 607, 757, 907, 11, 1210241, 2420471, 3630701, 4840931, 6051161, 7261391, 8471621, 11, 32671181, 65342351, 98013521, 130684691, 163355861, 196027031, 228698201, 261369371
Offset: 1

Views

Author

N. J. A. Sloane, Sep 22 2007, Oct 17 2007

Keywords

Comments

If we omit the first row, is this the same triangle as A113460? Equivalently, do A061558 and A113461 agree apart from the initial term? Answer: almost certainly not!

Examples

			Triangle begins:
2
2 3
3 5 7
5 11 17 23
5 11 17 23 29
7 37 67 97 127 157
7 157 307 457 607 757 907
11 1210241 2420471 3630701 4840931 6051161 7261391 8471621
11 32671181 65342351 98013521 130684691 163355861 196027031 228698201 261369371

Links

Crossrefs

For common differences see A061558.

Extensions

Extended by Ray Chandler, Sep 22 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.
Showing 1-5 of 5 results.

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

Content is available under The OEIS End-User License Agreement.