A179686 - OEIS

%I #8 May 11 2019 17:31:38

%S 1,2,4,2,2,2,4,2,6,4,4,6,8,6,4,2,4,10,4,6,2,4,12,12,4,14,12,2,14,14,4,

%T 2,18,12,16,4,8,16,16,14,18,4,12,4,4,4,20,10,6,22,24,4,26,6,16,6,20,4,

%U 12,26,8,22,4,2,34,8,20,14,34,24,32,6,20,42,4,12,8,10,24

%N Let m > k > 0 be odd numbers and operations "m<+>k" and "m<->k" be defined as in A179382 and A179480. Then the sequence m<+>k, m<->(m<+>k), m<+>(m<->(m<+>k)), ... is periodic; a(n) is its smallest period starting from the seeds m=2*n-1 and k=1.

%e If n=4, 2*n-1=7, then we have 7<+>1=1, 7<->1=3, 7<+>3=5, 7<->5=1. Thus a(4)=4.

%p pidx := proc(L,n,m)

%p     for i from 1 to nops(L)-1 do

%p         if [op(i..i+1,L)] = [n,m] then

%p             return i;

%p         end if;

%p     end do:

%p     return -1 ;

%p end proc:

%p A179686aux := proc(x, y) local xtrack, xitr, p;

%p     xtrack := [A000265(x+y)] ;

%p     while true do

%p         if type(nops(xtrack),'odd') then

%p             xitr := A000265(x-op(-1, xtrack)) ;

%p         else

%p             xitr := A000265(x+op(-1, xtrack)) ;

%p         end if;

%p             xtrack := [op(xtrack),xitr] ;

%p         p := pidx(xtrack,op(-2,xtrack),op(-1,xtrack)) ;

%p         if p >=1 and p < nops(xtrack) -2 then

%p             return nops(xtrack)-p-1 ;

%p         end if;

%p     end do:

%p end proc:

%p A179686 := proc(n)

%p     if n = 2 then

%p         1;

%p     else

%p         A179686aux(2*n-1,1) ;

%p     end if;

%p end proc:

%p seq(A179686(n),n=2..80) ; # _R. J. Mathar_, Dec 04 2011

%Y Cf. A179382, A179480.

%K nonn

%O 2,2

%A _Vladimir Shevelev_, Jul 24 2010

%E Extended beyond a(24) by _R. J. Mathar_, Dec 04 2011