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Revision as of 08:48, 11 January 2010
, 08:48, 11 January 2010→A108352
* \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
* \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
* 16 . . 14. 1 . 9 . 1 . 10. 1 . 1 . 1 . 6 . 1 . 2 . 1 . 2 . . 16
* 16 . . 14. 1 . 9 . 1 . 10. 1 . 1 . 1 . 6 . 1 . 2 . 1 . 2 . . 16
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==A108352==
* [http://oeis.org/wiki/A108352 A108352]
===Links===
* Jon Awbrey, [http://stderr.org/pipermail/inquiry/2005-July/002846.html Primal Code Characteristic, n = 1 to 1000]
* Jon Awbrey, [http://stderr.org/pipermail/inquiry/2005-July/002847.html Primal Code Characteristic, n = 1001 to 2000]
* Jon Awbrey, [http://stderr.org/pipermail/inquiry/2005-July/002853.html Primal Code Characteristic, n = 2001 to 3000]
===TeX Array===
{| align="center"
|
<math>\begin{array}{*{10}{l}}
a(1)
& = & 1
& \text{because} & (\circ~ 1)^1
& = & (\circ~ \varnothing)^1
& = & 1.
\\
a(2)
& = & 0
& \text{because} & (\circ~ 2)^k
& = & (\circ~ 1\!:\!1)^k
& = & 2,
& \text{for all}~ k > 0.
\\
a(3)
& = & 2
& \text{because} & (\circ~ 3)^2
& = & (\circ~ 2\!:\!1)^2
& = & 1.
\\
a(4)
& = & 2
& \text{because} & (\circ~ 4 )^2
& = & (\circ~ 1\!:\!2)^2
& = &1.
\\
a(5)
& = & 2
& \text{because} & (\circ~ 5)^2
& = & (\circ~ 3\!:\!1)^2
& = & 1.
\\
a(6)
& = & 0
& \text{because} & (\circ~ 6)^k
& = & (\circ~ 1\!:\!1 ~~ 2\!:\!1)^k
& = & 6,
& \text{for all}~ k > 0.
\\
a(7)
& = & 2
& \text{because} & (\circ~ 7)^2
& = & (\circ~ 4\!:\!1)^1
& = & 1.
\\
a(8)
& = & 2
& \text{because} & (\circ~ 8)^2
& = & (\circ~ 1\!:\!3)^1
& = & 1.
\\
a(9)
& = & 0
& \text{because} & (\circ~ 9)^k
& = & (\circ~ 2\!:\!2)^k
& = & 9,
& \text{for all}~ k > 0.
\\
a(10)
& = & 0
& \text{because} & (\circ~ 10)^k
& = & (\circ~ 1\!:\!1 ~~ 3\!:\!1)^k
& = & 10,
& \text{for all}~ k > 0.
\end{array}</math>
|}
===ASCII===
<pre>
Example
* a(1) = 1 because (1 o)^1 = ({ } o)^1 = 1.
* a(2) = 0 because (2 o)^k = (1:1 o)^k = 2, for all positive k.
* a(3) = 2 because (3 o)^2 = (2:1 o)^2 = 1.
* a(4) = 2 because (4 o)^2 = (1:2 o)^2 = 1.
* a(5) = 2 because (5 o)^2 = (3:1 o)^2 = 1.
* a(6) = 0 because (6 o)^k = (1:1 2:1 o)^k = 6, for all positive k.
* a(7) = 2 because (7 o)^2 = (4:1 o)^1 = 1.
* a(8) = 2 because (8 o)^2 = (1:3 o)^1 = 1.
* a(9) = 0 because (9 o)^k = (2:2 o)^k = 9, for all positive k.
* a(10) = 0 because (10 o)^k = (1:1 3:1 o)^k = 10, for all positive k.
* Detail of calculation for compositional powers of 12:
* (12 o)^2 = (1:2 2:1) o (1:2 2:1) = (1:1 2:2) = 18
* (12 o)^3 = (1:1 2:2) o (1:2 2:1) = (1:2 2:1) = 12
* Detail of calculation for compositional powers of 20:
* (20 o)^2 = (1:2 3:1) o (1:2 3:1) = (3:2) = 25
* (20 o)^3 = (3:2) o (1:2 3:1) = 1
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