A179787 Let the operation <+> be defined by x<+>y = A038502(x+y). a(n) is the period in the track of the iterated application x<+>(x<+>...(x<+>1)) for x = A001651(n-1).

2, 1, 2, 4, 6, 1, 4, 4, 2, 6, 3, 16, 18, 2, 3, 8, 20, 1, 6, 28, 30, 7, 16, 10, 18, 18, 2, 8, 42, 8, 11, 18, 42, 20, 4, 52, 20, 3, 28, 26, 10, 30, 15, 10, 22, 12, 8, 28, 12, 18, 18, 28, 78, 1, 8, 38, 14, 42, 9, 88, 4, 22, 23, 28, 48, 42, 18, 100, 34, 3, 52, 50, 22, 20, 9, 112, 38, 22, 23, 38

Offset: 1

Author

Vladimir Shevelev, Jul 27 2010

Keywords

• nonn

Comments

The symbol <+> removes powers of three of the sum of the two operands.

The process of starting with 1, adding some constant number x = A001651(n-1) and reducing it iteratively with this operation defines a track 1, x<+>1, x<+>(x<+>1), ... which enters a cycle.

The period of this cycle specifies a(n).

Similar iterated reductions can be defined for power bases m other than 3.

Examples

			For n=5 we take x=A001651(4)=7. The iteration yields 1, 7<+>1=8, 7<+>8=5, 7<+>5=4, 7<+>4=11, 7<+>11=2, 7<+>2=1.
We have reached the 1 of the beginning and therefore a cycle of length a(5)=6.
		

Crossrefs

Cf. A179382, A179480, A179686, A179738.

Programs

Maple

A038502 := proc(n) a := 1; for p in ifactors(n)[2] do if op(1,p) <> 3 then a := a*op(1,p)^op(2,p) ; end if; end do; a ; end proc:
A179787aux := proc(x,y) local xtrack,xitr,xpos ; xtrack := [y] ; while true do xitr := A038502(op(-1,xtrack)+x) ;
if not member(xitr, xtrack,'xpos') then xtrack := [op(xtrack),xitr] ; else return 1+nops(xtrack)-xpos ; end if; end do: end proc:
A001651 := proc(n) option remember; if n <=2 then n; else procname(n-2)+3 ; end if; end proc:
A179787 := proc(n) A179787aux(A001651(n),1) ; end proc: seq(A179787(n),n=1..80) ; # R. J. Mathar, Nov 04 2010

Extensions

a(22) corrected, definition tightened removing new terminology, sequence extended beyond a(55) by R. J. Mathar, Nov 04 2010