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A179787
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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).
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2
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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MAPLE
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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:
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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a(22) corrected, definition tightened removing new terminology, sequence extended beyond a(55) by R. J. Mathar, Nov 04 2010
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STATUS
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approved
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