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Revision as of 18:34, 23 January 2010
, 18:34, 23 January 2010no edit summary
<p><math>\text{p}_\text{p} \text{p}_{\text{p}_\text{p}} \text{p}_{\text{p}_{\text{p}_\text{p}}}\!</math></p><br>
<p><math>\text{p}_\text{p} \text{p}_{\text{p}_\text{p}} \text{p}_{\text{p}_{\text{p}_\text{p}}}\!</math></p><br>
<p><math>a(9) ~=~ 165</math></p>
<p><math>a(9) ~=~ 165</math></p>
|}
===A109301===
* '''a(n) = rhig(n) = rote height in gammas of n, where the "rote" corresponding to a positive integer n is a graph derived from the primes factorization of n, as illustrated in the comments.'''
* [http://oeis.org/wiki/A109301 OEIS Wiki Entry for A109301].
{| align="center" border="1" cellpadding="6"
|+ style="height:25px" | <math>a(n) = \text{Rote Height of}~ n</math>
| valign="bottom" |
<p>[[Image:Rote 1 Big.jpg|20px]]</p><br>
<p><math>1\!</math></p><br>
<p><math>a(1) ~=~ 0</math></p>
| valign="bottom" |
<p>[[Image:Rote 2 Big.jpg|40px]]</p><br>
<p><math>\text{p}\!</math></p><br>
<p><math>a(2) ~=~ 1</math></p>
| valign="bottom" |
<p>[[Image:Rote 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:Rote 4 Big.jpg|65px]]</p><br>
<p><math>\text{p}^\text{p}\!</math></p><br>
<p><math>a(4) ~=~ 2</math></p>
| valign="bottom" |
<p>[[Image:Rote 5 Big.jpg|40px]]</p><br>
<p><math>\text{p}_{\text{p}_\text{p}}\!</math></p><br>
<p><math>a(5) ~=~ 3</math></p>
|-
| valign="bottom" |
<p>[[Image:Rote 6 Big.jpg|80px]]</p><br>
<p><math>\text{p} \text{p}_\text{p}\!</math></p><br>
<p><math>a(6) ~=~ 2</math></p>
| valign="bottom" |
<p>[[Image:Rote 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:Rote 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:Rote 9 Big.jpg|80px]]</p><br>
<p><math>\text{p}_\text{p}^\text{p}\!</math></p><br>
<p><math>a(9) ~=~ 2</math></p>
| valign="bottom" |
<p>[[Image:Rote 10 Big.jpg|80px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p}_\text{p}}\!</math></p><br>
<p><math>a(10) ~=~ 3</math></p>
|-
| valign="bottom" |
<p>[[Image:Rote 11 Big.jpg|40px]]</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:Rote 12 Big.jpg|105px]]</p><br>
<p><math>\text{p}^\text{p} \text{p}_\text{p}\!</math></p><br>
<p><math>a(12) ~=~ 2</math></p>
| valign="bottom" |
<p>[[Image:Rote 13 Big.jpg|80px]]</p><br>
<p><math>\text{p}_{\text{p} \text{p}_\text{p}}\!</math></p><br>
<p><math>a(13) ~=~ 3</math></p>
| valign="bottom" |
<p>[[Image:Rote 14 Big.jpg|105px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p}^\text{p}}\!</math></p><br>
<p><math>a(14) ~=~ 3</math></p>
| valign="bottom" |
<p>[[Image:Rote 15 Big.jpg|80px]]</p><br>
<p><math>\text{p}_\text{p} \text{p}_{\text{p}_\text{p}}\!</math></p><br>
<p><math>a(15) ~=~ 3</math></p>
|-
| valign="bottom" |
<p>[[Image:Rote 16 Big.jpg|90px]]</p><br>
<p><math>\text{p}^{\text{p}^\text{p}}\!</math></p><br>
<p><math>a(16) ~=~ 3</math></p>
| valign="bottom" |
<p>[[Image:Rote 17 Big.jpg|65px]]</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:Rote 18 Big.jpg|120px]]</p><br>
<p><math>\text{p} \text{p}_\text{p}^\text{p}\!</math></p><br>
<p><math>a(18) ~=~ 2</math></p>
| valign="bottom" |
<p>[[Image:Rote 19 Big.jpg|65px]]</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:Rote 20 Big.jpg|105px]]</p><br>
<p><math>\text{p}^\text{p} \text{p}_{\text{p}_\text{p}}\!</math></p><br>
<p><math>a(20) ~=~ 3</math></p>
|-
| valign="bottom" |
<p>[[Image:Rote 21 Big.jpg|105px]]</p><br>
<p><math>\text{p}_\text{p} \text{p}_{\text{p}^\text{p}}\!</math></p><br>
<p><math>a(21) ~=~ 3</math></p>
| valign="bottom" |
<p>[[Image:Rote 22 Big.jpg|80px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p}_{\text{p}_\text{p}}}\!</math></p><br>
<p><math>a(22) ~=~ 4</math></p>
| valign="bottom" |
<p>[[Image:Rote 23 Big.jpg|80px]]</p><br>
<p><math>\text{p}_{\text{p}_\text{p}^\text{p}}\!</math></p><br>
<p><math>a(23) ~=~ 3</math></p>
| valign="bottom" |
<p>[[Image:Rote 24 Big.jpg|105px]]</p><br>
<p><math>\text{p}^{\text{p}_\text{p}} \text{p}_\text{p}\!</math></p><br>
<p><math>a(24) ~=~ 3</math></p>
| valign="bottom" |
<p>[[Image:Rote 25 Big.jpg|80px]]</p><br>
<p><math>\text{p}_{\text{p}_\text{p}}^\text{p}\!</math></p><br>
<p><math>a(25) ~=~ 3</math></p>
|-
| valign="bottom" |
<p>[[Image:Rote 26 Big.jpg|120px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p} \text{p}_\text{p}}\!</math></p><br>
<p><math>a(26) ~=~ 3</math></p>
| valign="bottom" |
<p>[[Image:Rote 27 Big.jpg|80px]]</p><br>
<p><math>\text{p}_\text{p}^{\text{p}_\text{p}}\!</math></p><br>
<p><math>a(27) ~=~ 3</math></p>
| valign="bottom" |
<p>[[Image:Rote 28 Big.jpg|130px]]</p><br>
<p><math>\text{p}^\text{p} \text{p}_{\text{p}^\text{p}}\!</math></p><br>
<p><math>a(28) ~=~ 3</math></p>
| valign="bottom" |
<p>[[Image:Rote 29 Big.jpg|80px]]</p><br>
<p><math>\text{p}_{\text{p} \text{p}_{\text{p}_\text{p}}}\!</math></p><br>
<p><math>a(29) ~=~ 4</math></p>
| valign="bottom" |
<p>[[Image:Rote 30 Big.jpg|120px]]</p><br>
<p><math>\text{p} \text{p}_\text{p} \text{p}_{\text{p}_\text{p}}\!</math></p><br>
<p><math>a(30) ~=~ 3</math></p>
|-
| valign="bottom" |
<p>[[Image:Rote 31 Big.jpg|40px]]</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:Rote 32 Big.jpg|65px]]</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:Rote 33 Big.jpg|80px]]</p><br>
<p><math>\text{p}_\text{p} \text{p}_{\text{p}_{\text{p}_\text{p}}}\!</math></p><br>
<p><math>a(33) ~=~ 4</math></p>
| valign="bottom" |
<p>[[Image:Rote 34 Big.jpg|105px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p}_{\text{p}^\text{p}}}\!</math></p><br>
<p><math>a(34) ~=~ 4</math></p>
| valign="bottom" |
<p>[[Image:Rote 35 Big.jpg|105px]]</p><br>
<p><math>\text{p}_{\text{p}_\text{p}} \text{p}_{\text{p}^\text{p}}\!</math></p><br>
<p><math>a(35) ~=~ 3</math></p>
|-
| valign="bottom" |
<p>[[Image:Rote 36 Big.jpg|145px]]</p><br>
<p><math>\text{p}^\text{p} \text{p}_\text{p}^\text{p}\!</math></p><br>
<p><math>a(36) ~=~ 2</math></p>
| valign="bottom" |
<p>[[Image:Rote 37 Big.jpg|105px]]</p><br>
<p><math>\text{p}_{\text{p}^\text{p} \text{p}_\text{p}}\!</math></p><br>
<p><math>a(37) ~=~ 3</math></p>
| valign="bottom" |
<p>[[Image:Rote 38 Big.jpg|105px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p}^{\text{p}_\text{p}}}\!</math></p><br>
<p><math>a(38) ~=~ 4</math></p>
| valign="bottom" |
<p>[[Image:Rote 39 Big.jpg|120px]]</p><br>
<p><math>\text{p}_\text{p} \text{p}_{\text{p} \text{p}_\text{p}}\!</math></p><br>
<p><math>a(39) ~=~ 3</math></p>
| valign="bottom" |
<p>[[Image:Rote 40 Big.jpg|105px]]</p><br>
<p><math>\text{p}^{\text{p}_\text{p}} \text{p}_{\text{p}_\text{p}}\!</math></p><br>
<p><math>a(40) ~=~ 3</math></p>
|-
| valign="bottom" |
<p>[[Image:Rote 41 Big.jpg|80px]]</p><br>
<p><math>\text{p}_{\text{p}_{\text{p} \text{p}_\text{p}}}\!</math></p><br>
<p><math>a(41) ~=~ 4</math></p>
| valign="bottom" |
<p>[[Image:Rote 42 Big.jpg|145px]]</p><br>
<p><math>\text{p} \text{p}_\text{p} \text{p}_{\text{p}^\text{p}}\!</math></p><br>
<p><math>a(42) ~=~ 3</math></p>
| valign="bottom" |
<p>[[Image:Rote 43 Big.jpg|105px]]</p><br>
<p><math>\text{p}_{\text{p} \text{p}_{\text{p}^\text{p}}}\!</math></p><br>
<p><math>a(43) ~=~ 4</math></p>
| valign="bottom" |
<p>[[Image:Rote 44 Big.jpg|105px]]</p><br>
<p><math>\text{p}^\text{p} \text{p}_{\text{p}_{\text{p}_\text{p}}}\!</math></p><br>
<p><math>a(44) ~=~ 4</math></p>
| valign="bottom" |
<p>[[Image:Rote 45 Big.jpg|120px]]</p><br>
<p><math>\text{p}_\text{p}^\text{p} \text{p}_{\text{p}_\text{p}}\!</math></p><br>
<p><math>a(45) ~=~ 3</math></p>
|-
| valign="bottom" |
<p>[[Image:Rote 46 Big.jpg|120px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p}_\text{p}^\text{p}}\!</math></p><br>
<p><math>a(46) ~=~ 3</math></p>
| valign="bottom" |
<p>[[Image:Rote 47 Big.jpg|80px]]</p><br>
<p><math>\text{p}_{\text{p}_\text{p} \text{p}_{\text{p}_\text{p}}}\!</math></p><br>
<p><math>a(47) ~=~ 4</math></p>
| valign="bottom" |
<p>[[Image:Rote 48 Big.jpg|105px]]</p><br>
<p><math>\text{p}^{\text{p}^\text{p}} \text{p}_\text{p}\!</math></p><br>
<p><math>a(48) ~=~ 3</math></p>
| valign="bottom" |
<p>[[Image:Rote 49 Big.jpg|80px]]</p><br>
<p><math>\text{p}_{\text{p}^\text{p}}^\text{p}\!</math></p><br>
<p><math>a(49) ~=~ 3</math></p>
| valign="bottom" |
<p>[[Image:Rote 50 Big.jpg|120px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p}_\text{p}}^\text{p}\!</math></p><br>
<p><math>a(50) ~=~ 3</math></p>
|-
| valign="bottom" |
<p>[[Image:Rote 51 Big.jpg|105px]]</p><br>
<p><math>\text{p}_\text{p} \text{p}_{\text{p}_{\text{p}^\text{p}}}\!</math></p><br>
<p><math>a(51) ~=~ 4</math></p>
| valign="bottom" |
<p>[[Image:Rote 52 Big.jpg|145px]]</p><br>
<p><math>\text{p}^\text{p} \text{p}_{\text{p} \text{p}_\text{p}}\!</math></p><br>
<p><math>a(52) ~=~ 3</math></p>
| valign="bottom" |
<p>[[Image:Rote 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:Rote 54 Big.jpg|120px]]</p><br>
<p><math>\text{p} \text{p}_\text{p}^{\text{p}_\text{p}}\!</math></p><br>
<p><math>a(54) ~=~ 3</math></p>
| valign="bottom" |
<p>[[Image:Rote 55 Big.jpg|80px]]</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) ~=~ 4</math></p>
|-
| valign="bottom" |
<p>[[Image:Rote 56 Big.jpg|130px]]</p><br>
<p><math>\text{p}^{\text{p}_\text{p}} \text{p}_{\text{p}^\text{p}}\!</math></p><br>
<p><math>a(56) ~=~ 3</math></p>
| valign="bottom" |
<p>[[Image:Rote 57 Big.jpg|105px]]</p><br>
<p><math>\text{p}_\text{p} \text{p}_{\text{p}^{\text{p}_\text{p}}}\!</math></p><br>
<p><math>a(57) ~=~ 4</math></p>
| valign="bottom" |
<p>[[Image:Rote 58 Big.jpg|120px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p} \text{p}_{\text{p}_\text{p}}}\!</math></p><br>
<p><math>a(58) ~=~ 4</math></p>
| valign="bottom" |
<p>[[Image:Rote 59 Big.jpg|65px]]</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:Rote 60 Big.jpg|155px]]</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) ~=~ 3</math></p>
|}
|}
