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.

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

Offset: 2

Author

Vladimir Shevelev, Jul 24 2010

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A179382, A179480.

Programs

Maple

pidx := proc(L,n,m)
    for i from 1 to nops(L)-1 do
        if [op(i..i+1,L)] = [n,m] then
            return i;
        end if;
    end do:
    return -1 ;
end proc:
A179686aux := proc(x, y) local xtrack, xitr, p;
    xtrack := [A000265(x+y)] ;
    while true do
        if type(nops(xtrack),'odd') then
            xitr := A000265(x-op(-1, xtrack)) ;
        else
            xitr := A000265(x+op(-1, xtrack)) ;
        end if;
            xtrack := [op(xtrack),xitr] ;
        p := pidx(xtrack,op(-2,xtrack),op(-1,xtrack)) ;
        if p >=1 and p < nops(xtrack) -2 then
            return nops(xtrack)-p-1 ;
        end if;
    end do:
end proc:
A179686 := proc(n)
    if n = 2 then
        1;
    else
        A179686aux(2*n-1,1) ;
    end if;
end proc:
seq(A179686(n),n=2..80) ; # R. J. Mathar, Dec 04 2011

Extensions

Extended beyond a(24) by R. J. Mathar, Dec 04 2011