A179787 - OEIS

%I #11 Nov 20 2023 00:04:11

%S 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,

%T 8,11,18,42,20,4,52,20,3,28,26,10,30,15,10,22,12,8,28,12,18,18,28,78,

%U 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

%N 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).

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

%C 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.

%C The period of this cycle specifies a(n).

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

%e 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.

%e We have reached the 1 of the beginning and therefore a cycle of length a(5)=6.

%p 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:

%p A179787aux := proc(x,y) local xtrack,xitr,xpos ; xtrack := [y] ; while true do xitr := A038502(op(-1,xtrack)+x) ;

%p if not member(xitr, xtrack,'xpos') then xtrack := [op(xtrack),xitr] ; else return 1+nops(xtrack)-xpos ; end if; end do: end proc:

%p A001651 := proc(n) option remember; if n <=2 then n; else procname(n-2)+3 ; end if; end proc:

%p A179787 := proc(n) A179787aux(A001651(n),1) ; end proc: seq(A179787(n),n=1..80) ; # _R. J. Mathar_, Nov 04 2010

%Y Cf. A179382, A179480, A179686, A179738.

%K nonn

%O 1,1

%A _Vladimir Shevelev_, Jul 27 2010

%E a(22) corrected, definition tightened removing new terminology, sequence extended beyond a(55) by _R. J. Mathar_, Nov 04 2010