User:Jon Awbrey/SEQUENCES - Revision history

Jon Awbrey: Undo revision 107256 by Jon Awbrey (Talk)

2010-01-31T18:48:18Z

Undo revision 107256 by Jon Awbrey (Talk)

Jon Awbrey at 17:48, 31 January 2010

2010-01-31T17:48:23Z

Jon Awbrey: /* A109301 */

2010-01-26T16:02:05Z

A109301

Jon Awbrey: /* A109301 */

2010-01-26T15:48:25Z

A109301

Jon Awbrey: /* A109301 */

2010-01-26T05:20:27Z

A109301

Jon Awbrey: /* A109301 */

2010-01-26T04:40:46Z

A109301

Jon Awbrey: /* A109301 */

2010-01-26T04:14:34Z

A109301

Jon Awbrey: /* A109301 */

2010-01-25T22:28:41Z

A109301

Jon Awbrey: /* A109301 */

2010-01-25T22:10:23Z

A109301

Jon Awbrey: /* Example */

2010-01-25T19:34:12Z

Example

@@ Line 8: / Line 8: @@
 {| align="center" border="1" cellpadding="12" cellspacing="1" style="text-align:center; width:96%"
-|+ style="height:24px" | <math>\text{Primes Factorizations, Riffs, Rotes, and Traversals}\!</math>
+|+ style="height:24px" | <math>\text{Prime Factorizations, Riffs, Rotes, and Traversals}\!</math>
 |- style="height:48px; background:#f0f0ff"
 | <math>\text{Integer}\!</math>
@@ Line 129: / Line 129: @@
 {| align="center" border="1" cellpadding="12" cellspacing="1" style="text-align:center; width:96%"
-|+ style="height:24px" | <math>\text{Primes Factorizations, Riffs, Rotes, and Traversals}\!</math>
+|+ style="height:24px" | <math>\text{Prime Factorizations, Riffs, Rotes, and Traversals}\!</math>
 |- style="height:48px; background:#f0f0ff"
 | <math>\text{Integer}\!</math>
@@ Line 252: / Line 252: @@
 {| align="center" border="1" width="96%"
-|+ style="height:24px" | <math>\text{Primes Factorizations, Riffs, Rotes, and Traversals}\!</math>
+|+ style="height:24px" | <math>\text{Prime Factorizations, Riffs, Rotes, and Traversals}\!</math>
 |- style="height:50px; background:#f0f0ff"
+|
@@ Line 388: / Line 388: @@
 {| align="center" border="1" width="96%"
-|+ style="height:24px" | <math>\text{Primes Factorizations, Riffs, Rotes, and Traversals}\!</math>
+|+ style="height:24px" | <math>\text{Prime Factorizations, Riffs, Rotes, and Traversals}\!</math>
 |- style="height:50px; background:#f0f0ff"
+|
@@ Line 1,045: / Line 1,045: @@
 {| align="center" border="1" width="90%"
-|+ style="height:25px" | <math>\text{Primes Factorizations, Riffs, and Rotes}\!</math>
+|+ style="height:25px" | <math>\text{Prime Factorizations, Riffs, and Rotes}\!</math>
 |- style="height:50px; background:#f0f0ff"
+|

@@ Line 8: / Line 8: @@
 {| align="center" border="1" cellpadding="12" cellspacing="1" style="text-align:center; width:96%"
-|+ style="height:24px" | <math>\text{Prime Factorizations, Riffs, Rotes, and Traversals}\!</math>
+|+ style="height:24px" | <math>\text{Primes Factorizations, Riffs, Rotes, and Traversals}\!</math>
 |- style="height:48px; background:#f0f0ff"
 | <math>\text{Integer}\!</math>
@@ Line 129: / Line 129: @@
 {| align="center" border="1" cellpadding="12" cellspacing="1" style="text-align:center; width:96%"
-|+ style="height:24px" | <math>\text{Prime Factorizations, Riffs, Rotes, and Traversals}\!</math>
+|+ style="height:24px" | <math>\text{Primes Factorizations, Riffs, Rotes, and Traversals}\!</math>
 |- style="height:48px; background:#f0f0ff"
 | <math>\text{Integer}\!</math>
@@ Line 252: / Line 252: @@
 {| align="center" border="1" width="96%"
-|+ style="height:24px" | <math>\text{Prime Factorizations, Riffs, Rotes, and Traversals}\!</math>
+|+ style="height:24px" | <math>\text{Primes Factorizations, Riffs, Rotes, and Traversals}\!</math>
 |- style="height:50px; background:#f0f0ff"
+|
@@ Line 388: / Line 388: @@
 {| align="center" border="1" width="96%"
-|+ style="height:24px" | <math>\text{Prime Factorizations, Riffs, Rotes, and Traversals}\!</math>
+|+ style="height:24px" | <math>\text{Primes Factorizations, Riffs, Rotes, and Traversals}\!</math>
 |- style="height:50px; background:#f0f0ff"
+|
@@ Line 1,045: / Line 1,045: @@
 {| align="center" border="1" width="90%"
-|+ style="height:25px" | <math>\text{Prime Factorizations, Riffs, and Rotes}\!</math>
+|+ style="height:25px" | <math>\text{Primes Factorizations, Riffs, and Rotes}\!</math>
 |- style="height:50px; background:#f0f0ff"
+|

@@ Line 2,507: / Line 2,507: @@
 ===Example===
-: <p><math>802701 = 9 \cdot 89189 = \text{p}_2^2 \text{p}_{8638}^1</math></p>
+: <math>802701 = 9 \cdot 89189 = \text{p}_2^2 \text{p}_{8638}^1</math>
-: <p><math>\text{Writing}~ (\operatorname{prime}(i))^j ~\text{as}~ i\!:\!j, ~\text{we have:}</math></p>
+: <math>\text{Writing}~ (\operatorname{prime}(i))^j ~\text{as}~ i\!:\!j, ~\text{we have:}</math>
-: <p><math>\begin{array}{lllll}
+: <math>\begin{array}{lllll}
 & = & 9 \cdot 89189
@@ Line 2,539: / Line 2,539: @@
 &   &
 & = & 1\!:\!1
-\end{array}</math></p>
+\end{array}</math>
-: <p><math>\text{So the rote of 802701 is the following graph:}</math></p>
+: <math>\text{So the rote of 802701 is the following graph:}\!</math>
 :{| border="1" cellpadding="20"
 | [[Image:Rote 802701 Big.jpg|330px]]
 |}
-: <p><math>\text{By inspection, the rote height of 802701 is 6.}</math></p>
 ===JPEG===

@@ Line 2,507: / Line 2,507: @@
 ===Example===
-<p><math>802701 = 9 \cdot 89189 = \text{p}_2^2 \text{p}_{8638}^1</math></p>
+: <p><math>802701 = 9 \cdot 89189 = \text{p}_2^2 \text{p}_{8638}^1</math></p>
-<p><math>\text{Writing}~ (\operatorname{prime}(i))^j ~\text{as}~ i\!:\!j, ~\text{we have:}</math></p>
+: <p><math>\text{Writing}~ (\operatorname{prime}(i))^j ~\text{as}~ i\!:\!j, ~\text{we have:}</math></p>
-<p><math>\begin{array}{lllll}
+: <p><math>\begin{array}{lllll}
 & = & 9 \cdot 89189
@@ Line 2,541: / Line 2,541: @@
 \end{array}</math></p>
-<p><math>\text{So}~ \operatorname{rote}(802701) ~\text{is the graph:}</math></p>
+: <p><math>\text{So the rote of 802701 is the following graph:}</math></p>
-{| align="center" border="1" cellpadding="20"
+:{| border="1" cellpadding="20"
 | [[Image:Rote 802701 Big.jpg|330px]]
 |}
+: <p><math>\text{By inspection, the rote height of 802701 is 6.}</math></p>
 ===JPEG===

@@ Line 2,507: / Line 2,507: @@
 ===Example===
-<math>802701 = 9 \cdot 89189 = \text{p}_2^2 \text{p}_{8638}^1</math>
+<p><math>802701 = 9 \cdot 89189 = \text{p}_2^2 \text{p}_{8638}^1</math></p>
-<math>\text{Writing}~ (\operatorname{prime}(i))^j ~\text{as}~ i\!:\!j, ~\text{we have:}</math>
+<p><math>\text{Writing}~ (\operatorname{prime}(i))^j ~\text{as}~ i\!:\!j, ~\text{we have:}</math></p>
-<math>\begin{array}{lllll}
+<p><math>\begin{array}{lllll}
 & = & 9 \cdot 89189
@@ Line 2,539: / Line 2,539: @@
 &   &
 & = & 1\!:\!1
-\end{array}</math>
+\end{array}</math></p>
-<math>\text{So}~ \operatorname{rote}(802701) ~\text{is the graph:}</math>
+<p><math>\text{So}~ \operatorname{rote}(802701) ~\text{is the graph:}</math></p>
 {| align="center" border="1" cellpadding="20"
@@ Line 2,547: / Line 2,547: @@
 |}
-<math>\text{Therefore, the rote height of}~ 802701 ~\text{is}~ 6.</math>
+<p><math>\text{Therefore, the rote height of}~ 802701 ~\text{is}~ 6.</math></p>
 ===JPEG===

@@ Line 2,511: / Line 2,511: @@
 <math>\text{Writing}~ (\operatorname{prime}(i))^j ~\text{as}~ i\!:\!j, ~\text{we have:}</math>
-<math>\begin{array}{lll}
+<math>\begin{array}{lllll}
 & = & 2\!:\!2 ~~ 8638\!:\!1
 \\
 & = & 1\!:\!1 ~~ 4\!:\!1 ~~ 113\!:\!1
 \\
 & = & 30\!:\!1
 \\
 & = & 1\!:\!1 ~~ 2\!:\!1 ~~ 3\!:\!1
 \\
 & = & 1\!:\!2
 \\
 & = & 2\!:\!1
 \\
 & = & 1\!:\!1
 \end{array}</math>

← Older revision		Revision as of 19:34, 25 January 2010
Line 2,508:		Line 2,508:

	<math>802701 = 9 \cdot 89189 = p_2^2 p_{8638}^1</math>		<math>802701 = 9 \cdot 89189 = p_2^2 p_{8638}^1</math>
		+
		+	<math>\text{Writing}~ (\operatorname{prime}(i))^j ~\text{as}~ i\!:\!j, ~\text{we have:}</math>
		+
		+	<math>\begin{array}{lll}
		+	802701 & = & 2\!:\!2 ~~ 8638\!:\!1
		+	\\
		+	8638 & = & 1\!:\!1 ~~ 4\!:\!1 ~~ 113\!:\!1
		+	\\
		+	113 & = & 30\!:\!1
		+	\\
		+	30 & = & 1\!:\!1 ~~ 2\!:\!1 ~~ 3\!:\!1
		+	\\
		+	4 & = & 1\!:\!2
		+	\\
		+	3 & = & 2\!:\!1
		+	\\
		+	2 & = & 1\!:\!1
		+	\end{array}</math>

	===JPEG===		===JPEG===