cp's OEIS Frontend

A179686 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.

%I A179686 #8 May 11 2019 17:31:38
%S A179686 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 A179686 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 A179686 12,26,8,22,4,2,34,8,20,14,34,24,32,6,20,42,4,12,8,10,24
%N A179686 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 A179686 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 A179686 pidx := proc(L,n,m)
%p A179686     for i from 1 to nops(L)-1 do
%p A179686         if [op(i..i+1,L)] = [n,m] then
%p A179686             return i;
%p A179686         end if;
%p A179686     end do:
%p A179686     return -1 ;
%p A179686 end proc:
%p A179686 A179686aux := proc(x, y) local xtrack, xitr, p;
%p A179686     xtrack := [A000265(x+y)] ;
%p A179686     while true do
%p A179686         if type(nops(xtrack),'odd') then
%p A179686             xitr := A000265(x-op(-1, xtrack)) ;
%p A179686         else
%p A179686             xitr := A000265(x+op(-1, xtrack)) ;
%p A179686         end if;
%p A179686             xtrack := [op(xtrack),xitr] ;
%p A179686         p := pidx(xtrack,op(-2,xtrack),op(-1,xtrack)) ;
%p A179686         if p >=1 and p < nops(xtrack) -2 then
%p A179686             return nops(xtrack)-p-1 ;
%p A179686         end if;
%p A179686     end do:
%p A179686 end proc:
%p A179686 A179686 := proc(n)
%p A179686     if n = 2 then
%p A179686         1;
%p A179686     else
%p A179686         A179686aux(2*n-1,1) ;
%p A179686     end if;
%p A179686 end proc:
%p A179686 seq(A179686(n),n=2..80) ; # _R. J. Mathar_, Dec 04 2011
%Y A179686 Cf. A179382, A179480.
%K A179686 nonn
%O A179686 2,2
%A A179686 _Vladimir Shevelev_, Jul 24 2010
%E A179686 Extended beyond a(24) by _R. J. Mathar_, Dec 04 2011