monotonic decrease of sinners (redemption)

[vdmcc]

dear Olivier and Neil,


my own generalisation about Sin[n] decreasing to -1 in a "dumb" way, by
1,3,4,5,11,344,1054,1764,2474,...
and so on with differences:
2,1,1,6,333,710,710,710...
is probably wrong. There are a lot of steps of size 710, but afterward it
changes !

for |cos(n)| decreasing to 0
1,2,5,8,11,344,699,1054,1409,...
again, it is "locally dumb", with differences
1,3,3,3,333,355,355...
and repeating the step size of 355 until  n=52174 (that's half of the by now
familiar 104348).
But here the stepsize changes to something bigger.
I couldn't find what size exactly.


wouter.






Neil,
addition to |sin| decreasing to 0
1,3,44,311,377,688,710,103638,104703

addition to sin decreasing to 0
1,3,22,333,355,103993,104348




-----Original Message-----
From: Olivier Gerard <ogerard at ext.jussieu.fr>
To: seqfan <seqfan at ext.jussieu.fr>
Date: Monday, April 19, 1999 5:16 PM
Subject: Re: monotonic decrease of sin (paradise version)


>At 18:53 +0200 99.04.19, vdmcc wrote:
>
>
>->Neil,
>->for what it's worth :
>->-------------------------------------------------------------------------
---
>->Sin[n] decreases monotonically to 0 :
>->
>->z={};current=1;
>->Timing[Do[
>->    If[If[(t=Sin[n])>0,t,1]<current,AppendTo[z,current=t ]],{n,105000 }]]
>->
>->{Sin[1],Sin[3],Sin[44],Sin[311],Sin[377],Sin[688],Sin[710],Sin[103638],
>->  Sin[104703]}
>->-------------------------------------------------------------------------
---
>->
>->Cos[n] decreases monotonically to -1 :
>->z={};current=1;
>->Timing[Do[If[Cos[n]<current,AppendTo[z,current=Cos[n]]],{n,105000}]]
>->
>->{Cos[1],Cos[2],Cos[3],Cos[22],Cos[355],Cos[104348]}
>->-------------------------------------------------------------------------
---
>->
>->Abs[Tan[n]] decreases monotonically to 0 :
>->z={};current=1;
>->Timing[Do[
>->    If[Abs[Tan[n]]<current,AppendTo[z,current=Abs[Tan[n]]]],{n,105000}]]
>->{-Tan[3],Tan[22],-Tan[333],Tan[355],-Tan[103993],Tan[104348]}
>->-------------------------------------------------------------------------
---
>
>So, I was too short of a few thousands, for the next term in the sparse
cases.
>One should always have one's best computer handy, but my portable is old
now.
>
>->So let's be carefull with Gerard's early generalisations (;-))
>->
>
>Wouter, I was considering decrease to 0 and not to -1.
>
>
>Olivier
>
>
>