Revision History for A090370
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
| older changes
|
| |
| |
| |
|
|
#23 by Giovanni Resta at Fri Aug 10 12:49:03 EDT 2018
| |
| |
| |
|
|
#22 by Michel Marcus at Fri Aug 10 01:54:03 EDT 2018
| |
| |
| |
|
|
#21 by Jon E. Schoenfield at Thu Aug 09 22:40:46 EDT 2018
| |
| |
| |
|
|
#20 by Jon E. Schoenfield at Thu Aug 09 22:40:43 EDT 2018
|
|
| NAME
|
Least m> > 3 such that gcd(n-1,, m*n - 1)=) = m-1.
|
|
| COMMENTS
|
Choosing a pair (m, n) so as to redefine 1 hour= = m*n minutes and 1 minute= = m*n seconds, then the three hands of a fictitious n-hour clock coincide in exactly m-1 equally spaced positions, including that of the n o'clock position. For instance, in the cases where we select (m, n) as (6, 11), (8, 15), (4, 25), with m*n respectively equal to 66, 120, 100 (implying 1 hour= = 66 minutes, 1 minute= = 66 seconds;; 1 hour= = 120 minutes, 1 minute= = 120 seconds;; 1 hour= = 100 minutes, 1 minute= = 100 seconds), the hands coincide in exactly 6-1=5, 8-1=7, 4-1=3 equally spaced positions on a 11-hour, 15-hour, 25-hour clock respectively.
|
|
| EXAMPLE
|
We have a(50)=8 because 50*8= = 400 is the least multiple of 50 such that ( gcd(50-1,, 400-1)=) = 8- - 1= = 7.
|
|
| STATUS
|
reviewed
editing
|
| |
| |
|
|
#19 by Giovanni Resta at Thu Aug 09 11:25:28 EDT 2018
| |
| |
| |
|
|
#18 by Michel Marcus at Thu Aug 09 10:40:13 EDT 2018
| |
| |
|
|
Discussion
|
| Thu Aug 09
| 10:40
| Michel Marcus: ok like this ?
|
|
| 10:48
| Søren Eilers: Looks great, thanks!
|
| |
| |
|
|
#17 by Michel Marcus at Thu Aug 09 10:40:03 EDT 2018
|
|
| FORMULA
|
a(n)=) = 1+ + A090368(k) for n=2k. a(n)=1+A090369(k) for. [corrected by _Søren Eilers_, Aug 09 n=2k+1.2018]
a(n) = 1 + A090369(k) for n=2k+1.
|
|
| MAPLE
|
A090370:=proc(n) local m; m:=4; while (gcd(n-1, m*n - 1) <> m-1) do m:=m+1; end; return m; end; _; # _Søren Eilers_, Aug 09 2018
|
|
| EXTENSIONS
|
Relation to A090368 as well as a(46) and a(49) corrected, _ by _Søren Eilers_, Aug 09 2018
|
|
| STATUS
|
proposed
editing
|
| |
| |
|
|
#16 by Giovanni Resta at Thu Aug 09 10:34:35 EDT 2018
| |
| |
| |
|
|
#15 by Giovanni Resta at Thu Aug 09 10:34:26 EDT 2018
|
|
| LINKS
|
Giovanni Resta, <a href="/A090370/b090370.txt">Table of n, a(n) for n = 4..10000</a>
|
|
| MATHEMATICA
|
a[n_] := Block[{m=4}, While[GCD[n-1, n*m-1] != m-1, m++]; m]; Table[a[k], {k, 4, 67}] (* Giovanni Resta, Aug 09 2018 *)
|
|
| STATUS
|
proposed
editing
|
| |
| |
|
|
#14 by Søren Eilers at Thu Aug 09 09:41:42 EDT 2018
| |
| |
|
|
Discussion
|
| Thu Aug 09
| 10:35
| Michel Marcus: If I had searched the terms resulting from pari output, I would not have found this entry; and so I would have seen that there was a problem somewhere
|
| |
| |
|
|
