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A089756 a(1)=1 and a(i+1)=a(i)+9 if a(i)<=35, and a(i+1)=a(i)-35 if a(i)>35.

%I A089756 #16 May 10 2020 14:27:45
%S A089756 1,10,19,28,37,2,11,20,29,38,3,12,21,30,39,4,13,22,31,40,5,14,23,32,
%T A089756 41,6,15,24,33,42,7,16,25,34,43,8,17,26,35,44,9,18,27,36,1,10,19,28,
%U A089756 37,2,11,20,29,38,3,12,21,30,39,4,13,22,31,40,5,14,23,32,41,6,15,24,33,42,7,16,25,34,43,8,17
%N A089756 a(1)=1 and a(i+1)=a(i)+9 if a(i)<=35, and a(i+1)=a(i)-35 if a(i)>35.
%C A089756 Infinite cyclic sequence with a(44*j+k)=a(k) and 0 < k < 45 with all and only one time the 44th first integers > 0.
%C A089756 Periodic with period = 44. - _Harvey P. Dale_, Nov 04 2019
%H A089756 <a href="/index/Rec#order_44">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).
%p A089756 A089756 := proc(n)
%p A089756     option remember;
%p A089756     if n = 1 then
%p A089756         1;
%p A089756     else
%p A089756         if procname(n-1) > 35 then
%p A089756             procname(n-1)-35 ;
%p A089756         else
%p A089756             procname(n-1)+9 ;
%p A089756         end if;
%p A089756     end if;
%p A089756 end proc:
%p A089756 seq(A089756(n),n=1..100) ; # _R. J. Mathar_, Feb 28 2019
%t A089756 NestList[If[#<36,#+9,#-35]&,1,80] (* _Harvey P. Dale_, Nov 04 2019 *)
%K A089756 nonn,easy,less
%O A089756 1,2
%A A089756 _Pierre CAMI_, Jan 08 2004