# seqs needed

N. J. A. Sloane njas at research.att.com
Sun Apr 18 18:29:11 CEST 1999

```dear sequence fans:

a question from a correspondent suggested these 2 sequences,
which need more terms:

%I A046946
%S A046946 1,3,44,311,377,688,710
%N A046946 Sin(n) decreaes monotonically to 0.
%O A046946 0,2
%K A046946 nonn,nice,more
%A A046946 njas
%D A046946 Suggested by a question from Alan Walker (Alan_Walker at sabre.com)
%Y A046947 Cf. A046947;

%I A046947
%S A046947 1,3,22,333,355
%N A046947 |Sin(n)| decreaes monotonically to 0.
%O A046947 0,2
%K A046947 nonn,nice,more
%A A046947 njas
%p A046947 Digits:=50; M:=10000;  a:=[1]; R:=sin(1.); for n from 2 to M do t1:=evalf(sin(n)); if abs(t1)<R then R:
=abs(t1);  a:=[op(a),n]; fi; od: a;
%D A046947 Suggested by a question from Alan Walker (Alan_Walker at sabre.com)

the second sequence is closely related to
the numerators of the continued
fraction quotients to Pi, which are:

s1 := [3, 22, 333, 355, 103993, 104348, 208341, 312689, 833719, 1146408, 4272943, 5419351, 80143857,

165707065, 245850922, 411557987, 1068966896, 2549491779]

for which sin( ) gives:

[.141120008059867222, -.00885130929040387592, -.00882116611388587701, -.0000301443533594884492,

-5                        -5
-.0000191293357784237502, -.0000110150175842405569, .811431819503807721 10  , .290069938933211100 10  ,

-5                         -6                         -6                         -7
.231291941645270150 10  , -.587779972881381232 10  , -.549579497810490801 10  , -.382004750708966019 10  ,

-7                         -8                        -8                        -8
-.147728468179659086 10  , -.865478143496479273 10  , .611806538300111631 10  , .253671605196367648 10  ,

-8                        -9
.104463327907376339 10  , .447449493816149707 10  ]

anyway, what i am writing about is to request that someone
compute some more sequences of this type.  Namely,
the sequence of n's such that:

cos n falls monotoniaclly from cos(1) to 0
|cos(n)| """""""""""""""""""""""""""""""""
same thing for tan, sec, csc, cot, cosh, sinh, tanh, etc

then

same thing for
sin n rises monotonically from sin(1)
- and same for cos tan etc etc

Thanks!

Neil J. A. Sloane, njas at research.att.com,
AT&T Shannon Lab, 180 Park Ave, Room C233,
Florham Park, NJ 07932-0971 USA.