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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
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.
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
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