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

1,1

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.

Links

Table of n, a(n) for n=1..80.

Example

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.

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

Crossrefs

Cf. A179382, A179480, A179686, A179738.

Sequence in context: A284001 A139145 A201635 * A358918 A368058 A324225

Adjacent sequences: A179784 A179785 A179786 * A179788 A179789 A179790

Keyword

nonn

Author

Vladimir Shevelev, Jul 27 2010

Extensions

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

Status

approved