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Revision as of 14:46, 19 January 2010
, 14:46, 19 January 2010→Selected Sequences
4 & \{ 10, 11, 12, 13, 14, 17, 18, 19, 23, 25, 27, 32, 49, 53, 64, 81, 128, 256, 512, 65536 \} & 20
4 & \{ 10, 11, 12, 13, 14, 17, 18, 19, 23, 25, 27, 32, 49, 53, 64, 81, 128, 256, 512, 65536 \} & 20
\end{array}</math>
\end{array}</math>
|}
===A062537===
* '''Nodes in riff (rooted index-functional forest) for n.'''
* [http://oeis.org/wiki/A062537 OEIS Wiki Entry for A062537].
{| align="center" border="1" cellpadding="10"
|+ style="height:25px" | <math>a(n) = \text{Number of Nodes in the Riff of}~ n</math>
| valign="bottom" |
<p> </p><br>
<p> </p><br>
<p><math>a(1) ~=~ 0</math></p>
| valign="bottom" |
<p>[[Image:Riff 2 Big.jpg|20px]]</p><br>
<p><math>\text{p}\!</math></p><br>
<p><math>a(2) ~=~ 1</math></p>
| valign="bottom" |
<p>[[Image:Riff 3 Big.jpg|40px]]</p><br>
<p><math>\text{p}_\text{p}\!</math></p><br>
<p><math>a(3) ~=~ 2</math></p>
| valign="bottom" |
<p>[[Image:Riff 4 Big.jpg|40px]]</p><br>
<p><math>\text{p}^\text{p}\!</math></p><br>
<p><math>a(4) ~=~ 2</math></p>
| valign="bottom" |
<p>[[Image:Riff 5 Big.jpg|65px]]</p><br>
<p><math>\text{p}_{\text{p}_{\text{p}}}\!</math></p><br>
<p><math>a(5) ~=~ 3</math></p>
|-
| valign="bottom" |
<p>[[Image:Riff 6 Big.jpg|65px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p}}\!</math></p><br>
<p><math>a(6) ~=~ 3</math></p>
| valign="bottom" |
<p>[[Image:Riff 7 Big.jpg|65px]]</p><br>
<p><math>\text{p}_{\text{p}^{\text{p}}}\!</math></p><br>
<p><math>a(7) ~=~ 3</math></p>
| valign="bottom" |
<p>[[Image:Riff 8 Big.jpg|65px]]</p><br>
<p><math>\text{p}^{\text{p}_{\text{p}}}\!</math></p><br>
<p><math>a(8) ~=~ 3</math></p>
| valign="bottom" |
<p>[[Image:Riff 9 Big.jpg|40px]]</p><br>
<p><math>\text{p}_\text{p}^\text{p}\!</math></p><br>
<p><math>a(9) ~=~ 3</math></p>
| valign="bottom" |
<p>[[Image:Riff 10 Big.jpg|90px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p}_{\text{p}}}\!</math></p><br>
<p><math>a(10) ~=~ 4</math></p>
|-
| valign="bottom" |
<p>[[Image:Riff 11 Big.jpg|90px]]</p><br>
<p><math>\text{p}_{\text{p}_{\text{p}_{\text{p}}}}\!</math></p><br>
<p><math>a(11) ~=~ 4</math></p>
| valign="bottom" |
<p>[[Image:Riff 12 Big.jpg|65px]]</p><br>
<p><math>\text{p}^\text{p} \text{p}_\text{p}\!</math></p><br>
<p><math>a(12) ~=~ 4</math></p>
| valign="bottom" |
<p>[[Image:Riff 13 Big.jpg|65px]]</p><br>
<p><math>\text{p}_{\text{p} \text{p}_{\text{p}}}\!</math></p><br>
<p><math>a(13) ~=~ 4</math></p>
| valign="bottom" |
<p>[[Image:Riff 14 Big.jpg|90px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p}^{\text{p}}}\!</math></p><br>
<p><math>a(14) ~=~ 4</math></p>
| valign="bottom" |
<p>[[Image:Riff 15 Big.jpg|90px]]</p><br>
<p><math>\text{p}_\text{p} \text{p}_{\text{p}_{\text{p}}}\!</math></p><br>
<p><math>a(15) ~=~ 5</math></p>
|-
| valign="bottom" |
<p>[[Image:Riff 16 Big.jpg|65px]]</p><br>
<p><math>\text{p}^{\text{p}^{\text{p}}}\!</math></p><br>
<p><math>a(16) ~=~ 3</math></p>
| valign="bottom" |
<p>[[Image:Riff 17 Big.jpg|90px]]</p><br>
<p><math>\text{p}_{\text{p}_{\text{p}^{\text{p}}}}\!</math></p><br>
<p><math>a(17) ~=~ 4</math></p>
| valign="bottom" |
<p>[[Image:Riff 18 Big.jpg|65px]]</p><br>
<p><math>\text{p} \text{p}_\text{p}^\text{p}\!</math></p><br>
<p><math>a(18) ~=~ 4</math></p>
| valign="bottom" |
<p>[[Image:Riff 19 Big.jpg|90px]]</p><br>
<p><math>\text{p}_{\text{p}^{\text{p}_{\text{p}}}}\!</math></p><br>
<p><math>a(19) ~=~ 4</math></p>
| valign="bottom" |
<p>[[Image:Riff 20 Big.jpg|90px]]</p><br>
<p><math>\text{p}^\text{p} \text{p}_{\text{p}_{\text{p}}}\!</math></p><br>
<p><math>a(20) ~=~ 5</math></p>
|-
| valign="bottom" |
<p>[[Image:Riff 21 Big.jpg|90px]]</p><br>
<p><math>\text{p}_\text{p} \text{p}_{\text{p}^\text{p}}\!</math></p><br>
<p><math>a(21) ~=~ 5</math></p>
| valign="bottom" |
<p>[[Image:Riff 22 Big.jpg|115px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p}_{\text{p}_\text{p}}}\!</math></p><br>
<p><math>a(22) ~=~ 5</math></p>
| valign="bottom" |
<p>[[Image:Riff 23 Big.jpg|65px]]</p><br>
<p><math>\text{p}_{\text{p}_\text{p}^\text{p}}\!</math></p><br>
<p><math>a(23) ~=~ 4</math></p>
| valign="bottom" |
<p>[[Image:Riff 24 Big.jpg|115px]]</p><br>
<p><math>\text{p}^{\text{p}_\text{p}} \text{p}_\text{p}\!</math></p><br>
<p><math>a(24) ~=~ 5</math></p>
| valign="bottom" |
<p>[[Image:Riff 25 Big.jpg|65px]]</p><br>
<p><math>\text{p}_{\text{p}_\text{p}}^\text{p}\!</math></p><br>
<p><math>a(25) ~=~ 4</math></p>
|-
| valign="bottom" |
<p>[[Image:Riff 26 Big.jpg|90px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p} \text{p}_\text{p}}\!</math></p><br>
<p><math>a(26) ~=~ 5</math></p>
| valign="bottom" |
<p>[[Image:Riff 27 Big.jpg|65px]]</p><br>
<p><math>\text{p}_\text{p}^{\text{p}_\text{p}}\!</math></p><br>
<p><math>a(27) ~=~ 4</math></p>
| valign="bottom" |
<p>[[Image:Riff 28 Big.jpg|90px]]</p><br>
<p><math>\text{p}^\text{p} \text{p}_{\text{p}^\text{p}}\!</math></p><br>
<p><math>a(28) ~=~ 5</math></p>
| valign="bottom" |
<p>[[Image:Riff 29 Big.jpg|90px]]</p><br>
<p><math>\text{p}_{\text{p} \text{p}_{\text{p}_\text{p}}}\!</math></p><br>
<p><math>a(29) ~=~ 5</math></p>
| valign="bottom" |
<p>[[Image:Riff 30 Big.jpg|115px]]</p><br>
<p><math>\text{p} \text{p}_\text{p} \text{p}_{\text{p}_\text{p}}\!</math></p><br>
<p><math>a(30) ~=~ 6</math></p>
|-
| valign="bottom" |
<p>[[Image:Riff 31 Big.jpg|115px]]</p><br>
<p><math>\text{p}_{\text{p}_{\text{p}_{\text{p}_\text{p}}}}\!</math></p><br>
<p><math>a(31) ~=~ 5</math></p>
| valign="bottom" |
<p>[[Image:Riff 32 Big.jpg|90px]]</p><br>
<p><math>\text{p}^{\text{p}_{\text{p}_\text{p}}}\!</math></p><br>
<p><math>a(32) ~=~ 4</math></p>
| valign="bottom" |
<p>[[Image:Riff 33 Big.jpg|115px]]</p><br>
<p><math>\text{p}_\text{p} \text{p}_{\text{p}_{\text{p}_\text{p}}}\!</math></p><br>
<p><math>a(33) ~=~ 6</math></p>
| valign="bottom" |
<p>[[Image:Riff 34 Big.jpg|115px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p}_{\text{p}^\text{p}}}\!</math></p><br>
<p><math>a(34) ~=~ 5</math></p>
| valign="bottom" |
<p>[[Image:Riff 35 Big.jpg|90px]]</p><br>
<p><math>\text{p}_{\text{p}_\text{p}} \text{p}_{\text{p}^\text{p}}\!</math></p><br>
<p><math>a(35) ~=~ 6</math></p>
|-
| valign="bottom" |
<p>[[Image:Riff 36 Big.jpg|65px]]</p><br>
<p><math>\text{p}^\text{p} \text{p}_\text{p}^\text{p}\!</math></p><br>
<p><math>a(36) ~=~ 5</math></p>
| valign="bottom" |
<p>[[Image:Riff 37 Big.jpg|65px]]</p><br>
<p><math>\text{p}_{\text{p}^\text{p} \text{p}_\text{p}}\!</math></p><br>
<p><math>a(37) ~=~ 5</math></p>
| valign="bottom" |
<p>[[Image:Riff 38 Big.jpg|115px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p}^{\text{p}_\text{p}}}\!</math></p><br>
<p><math>a(38) ~=~ 5</math></p>
| valign="bottom" |
<p>[[Image:Riff 39 Big.jpg|115px]]</p><br>
<p><math>\text{p}_\text{p} \text{p}_{\text{p} \text{p}_\text{p}}\!</math></p><br>
<p><math>a(39) ~=~ 6</math></p>
| valign="bottom" |
<p>[[Image:Riff 40 Big.jpg|135px]]</p><br>
<p><math>\text{p}^{\text{p}_\text{p}} \text{p}_{\text{p}_\text{p}}\!</math></p><br>
<p><math>a(40) ~=~ 6</math></p>
|-
| valign="bottom" |
<p>[[Image:Riff 41 Big.jpg|90px]]</p><br>
<p><math>\text{p}_{\text{p}_{\text{p} \text{p}_\text{p}}}\!</math></p><br>
<p><math>a(41) ~=~ 5</math></p>
| valign="bottom" |
<p>[[Image:Riff 42 Big.jpg|115px]]</p><br>
<p><math>\text{p} \text{p}_\text{p} \text{p}_{\text{p}^\text{p}}\!</math></p><br>
<p><math>a(42) ~=~ 6</math></p>
| valign="bottom" |
<p>[[Image:Riff 43 Big.jpg|90px]]</p><br>
<p><math>\text{p}_{\text{p} \text{p}_{\text{p}^\text{p}}}\!</math></p><br>
<p><math>a(43) ~=~ 5</math></p>
| valign="bottom" |
<p>[[Image:Riff 44 Big.jpg|115px]]</p><br>
<p><math>\text{p}^\text{p} \text{p}_{\text{p}_{\text{p}_\text{p}}}\!</math></p><br>
<p><math>a(44) ~=~ 6</math></p>
| valign="bottom" |
<p>[[Image:Riff 45 Big.jpg|90px]]</p><br>
<p><math>\text{p}_\text{p}^\text{p} \text{p}_{\text{p}_\text{p}}\!</math></p><br>
<p><math>a(45) ~=~ 6</math></p>
|-
| valign="bottom" |
<p>[[Image:Riff 46 Big.jpg|90px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p}_\text{p}^\text{p}}\!</math></p><br>
<p><math>a(46) ~=~ 5</math></p>
| valign="bottom" |
<p>[[Image:Riff 47 Big.jpg|90px]]</p><br>
<p><math>\text{p}_{\text{p}_\text{p} \text{p}_{\text{p}_\text{p}}}\!</math></p><br>
<p><math>a(47) ~=~ 6</math></p>
| valign="bottom" |
<p>[[Image:Riff 48 Big.jpg|65px]]</p><br>
<p><math>\text{p}^{\text{p}^\text{p}} \text{p}_\text{p}\!</math></p><br>
<p><math>a(48) ~=~ 5</math></p>
| valign="bottom" |
<p>[[Image:Riff 49 Big.jpg|65px]]</p><br>
<p><math>\text{p}_{\text{p}^\text{p}}^\text{p}\!</math></p><br>
<p><math>a(49) ~=~ 4</math></p>
| valign="bottom" |
<p>[[Image:Riff 50 Big.jpg|90px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p}_\text{p}}^\text{p}\!</math></p><br>
<p><math>a(50) ~=~ 5</math></p>
|-
| valign="bottom" |
<p>[[Image:Riff 51 Big.jpg|115px]]</p><br>
<p><math>\text{p}_\text{p} \text{p}_{\text{p}_{\text{p}^\text{p}}}\!</math></p><br>
<p><math>a(51) ~=~ 6</math></p>
| valign="bottom" |
<p>[[Image:Riff 52 Big.jpg|90px]]</p><br>
<p><math>\text{p}^\text{p} \text{p}_{\text{p} \text{p}_\text{p}}\!</math></p><br>
<p><math>a(52) ~=~ 6</math></p>
| valign="bottom" |
<p>[[Image:Riff 53 Big.jpg|90px]]</p><br>
<p><math>\text{p}_{\text{p}^{\text{p}^\text{p}}}\!</math></p><br>
<p><math>a(53) ~=~ 4</math></p>
| valign="bottom" |
<p>[[Image:Riff 54 Big.jpg|90px]]</p><br>
<p><math>\text{p} \text{p}_\text{p}^{\text{p}_\text{p}}\!</math></p><br>
<p><math>a(54) ~=~ 5</math></p>
| valign="bottom" |
<p>[[Image:Riff 55 Big.jpg|115px]]</p><br>
<p><math>\text{p}_{\text{p}_\text{p}} \text{p}_{\text{p}_{\text{p}_\text{p}}}\!</math></p><br>
<p><math>a(55) ~=~ 7</math></p>
|-
| valign="bottom" |
<p>[[Image:Riff 56 Big.jpg|135px]]</p><br>
<p><math>\text{p}^{\text{p}_\text{p}} \text{p}_{\text{p}^\text{p}}\!</math></p><br>
<p><math>a(56) ~=~ 6</math></p>
| valign="bottom" |
<p>[[Image:Riff 57 Big.jpg|115px]]</p><br>
<p><math>\text{p}_\text{p} \text{p}_{\text{p}^{\text{p}_\text{p}}}\!</math></p><br>
<p><math>a(57) ~=~ 6</math></p>
| valign="bottom" |
<p>[[Image:Riff 58 Big.jpg|115px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p} \text{p}_{\text{p}_\text{p}}}\!</math></p><br>
<p><math>a(58) ~=~ 6</math></p>
| valign="bottom" |
<p>[[Image:Riff 59 Big.jpg|115px]]</p><br>
<p><math>\text{p}_{\text{p}_{\text{p}_{\text{p}^\text{p}}}}\!</math></p><br>
<p><math>a(59) ~=~ 5</math></p>
| valign="bottom" |
<p>[[Image:Riff 60 Big.jpg|115px]]</p><br>
<p><math>\text{p}^\text{p} \text{p}_\text{p} \text{p}_{\text{p}_\text{p}}\!</math></p><br>
<p><math>a(60) ~=~ 7</math></p>
|}
|}
