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 1-3 of 3 results.

A109473 Let m = n-th squarefree number = A005117(n), and consider the smallest pair of consecutive squarefree numbers (r,s) with gcd(r,s) = m; sequence gives values of r.

Original entry on oeis.org

1, 422, 174, 22830, 9216772051242, 234374
Offset: 1

Views

Author

N. J. A. Sloane, based on a suggestion from David W. Wilson, Aug 20 2005

Keywords

Comments

a(7) is the first unknown value.
If m (in the table in Examples) is odd then a(m) >= A020754(m-1). If m is even then a(m) >= A020754(2m-1). - Jud McCranie, Sep 30 2020
a(12) (for m=17) is greater than 3.3*10^16. - Jud McCranie, Oct 16 2020

Examples

			n  |  m |    a(n) = r
---+----+---------------
1  |  1 |              1
2  |  2 |            422
3  |  3 |            174
4  |  5 |          22830
5  |  6 |  9216772051242
6  |  7 |         234374
7  | 10 |              ?
8  | 11 |    21971536246
9  | 13 |  8678016978774
10 | 14 |              ?
11 | 15 | 36442589727570
Specifically, 174 is squarefree, 177 is the next squarefree integer, and gcd(174,177) = 3; this is the first pair of consecutive squarefree numbers whose GCD is 3, so a(3)=174. - _Jud McCranie_, Nov 25 2019

Crossrefs

See A109505 for another version. Cf. A005117, A051681, A020754, A337914, A337915.

Extensions

a(5) from Jud McCranie, Aug 28 2005
a(8) from Jud McCranie, Aug 29 2005 (see Examples)
a(9) from Jud McCranie, Aug 31 2005 (see Examples)
Don Reble pointed out that the value of a(5), 9216772051254, given in the DATA section should have been 9216772051242, as in the EXAMPLE section. Revised definition to clarify the difference between n and m. - N. J. A. Sloane, Nov 25 2019
a(11) from Jud McCranie, Sep 30 2020 (see Examples)

A109505 Consider the smallest pair of consecutive squarefree numbers (r,s) with gcd(r,s) = n; sequence gives values of r, or -1 if n is not squarefree.

Original entry on oeis.org

1, 422, 174, -1, 22830, 9216772051242, 234374, -1, -1
Offset: 1

Views

Author

N. J. A. Sloane, Aug 31 2005

Keywords

Comments

a(10) <= 462850319999160398264270. - David A. Corneth, Sep 19 2020
If n is odd then a(n) >= A020754(n-1). If n is even then a(n) >= A020754(2n-1). - Jud McCranie, Sep 30 2020

Examples

			174 is squarefree, 177 is the next squarefree integer, and gcd(174,177) = 3; this is the first pair of consecutive squarefree numbers whose GCD is 3, so a(3)=174. - _Jud McCranie_, Nov 25 2019

Crossrefs

See A109473, the main entry for this sequence, for more information.
Cf. A020754, A337914, A337915.

Extensions

a(6) corrected by Don Reble. - N. J. A. Sloane, Nov 25 2019

A337915 Squarefree multiples of 15 such that a(n)+15 is also squarefree and all integers between are not squarefree.

Original entry on oeis.org

36442589727570, 59068995605115, 70458333341415, 93553802716515, 99321073884915, 104575423448670, 225934088816670, 241427108122215, 245679971474670, 257496300981015, 263154806220570, 275458942061070, 312686748592170, 425667633054315, 448345051339515
Offset: 1

Views

Author

Jud McCranie, Oct 06 2020

Keywords

Comments

The terms are congruent to 15 or 870 mod 900 (900=2^2*3^2*5^2). The term a(1) is A109505(15) and A109473(10).

Links

Crossrefs

Cf. A337914.
Showing 1-3 of 3 results.

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

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