entry 17 tpo = termposition [ note: in this sequence, the subtrahend square root = the tpo ] [ note: minuend square root + subtrahend square root = remainder ] [ note: each term in this sequence is a positive odd whole number (pown) ] [ note: had this sequence begun with 1² - 0² = 1, the minuend square root would have equalled the tpo ] 2² - 1² = 3 3² - 2² = 5 4² - 3² = 7 5² - 4² = 9 = 3² 6² - 5² = 11 7² - 6² = 13 8² - 7² = 15 = 3 x 5 9² - 8² = 17 10² - 9² = 19 11² - 10² = 21 = 3 x 7 12² - 11² = 23 13² - 12² = 25 = 5² 14² - 13² = 27 = 3 x 9 = 3 x 3² 15² - 14² = 29 16² - 15² = 31 17² - 16² = 33 = 3 x 11 18² - 17² = 35 = 5 x 7 19² - 18² = 37 20² - 19² = 39 = 3 x 13 21² - 20² = 41 22² - 21² = 43 23² - 22² = 45 = 5 x 9 = 3 x 15 24² - 23² = 47 25² - 24² = 49 = 7² 26² - 25² = 51 = 3 x 17 # re: 3² tpo 2 and tpo 4 1 x 4 = 4 also: 2 + 4 = 6 re: 5² tpo 4 and tpo 12 3 x 4 = 12 also; 4 + 12 = 16 re: 7² tpo 6 and tpo 24 6 x 4 = 24 also: 6 + 24 = 30 lunch break [ note: (2 x 4) + 1 = 9 (4 x 6) + 1 = 25 (6 x 8) + 1 = 49 ] # 27² - 26² = 53 28² - 27² = 55 = 5 x 11 29² - 28² = 57 = 3 x 19 30² - 29² = 59 31² - 30² = 61 32² - 31² = 63 = 7 x 9 = 3 x 21 33² - 32² = 65 = 5 x 13 34² - 33² = 67 35² - 34² = 69 = 3 x 23 36² - 35² = 71 37² - 36² = 73 38² - 37² = 75 = 5 x 15 = 3 x 25 39² - 38² = 77 = 7 x 11 40² - 39² = 79 41² - 40² = 81 = 9 x 9 = 3 x 27 42² - 41² = 83 43² - 42² = 85 = 5 x 17 44² - 43² = 87 = 3 x 29 45² - 44² = 89 46² - 45² = 91 = 7 x 13 47² - 46² = 93 = 3 x 31 48² - 47² = 95 = 5 x 19 49² - 48² = 97 50² - 49² = 99 = 9 x 11 = 3 x 33 51² - 50² = 101 52² - 51² = 103 53² - 52² = 105 = 7 x 15 = 5 x 21 = 3 x 35 54² - 53² = 107 55² - 54² = 109 56² - 55² = 111 = 3 x 37 57² - 56² = 113 58² - 57² = 115 = 5 x 23 59² - 58² = 117 = 3 x 39 60² - 59² = 119 = 7 x 17 61² - 60² = 121 = 11 x 11 # [ note: if zero is included in the natural number summation sequence, any pown square minus 1 will equal a pewn which (when divided by 8) equals a term in the nnss -- example: 81 - 1 = 80; 80/8 = 10 as in: 0 + 1 = 1; 1 + 2 = 3; 3 + 3 = 6; 6 + 4 = 10 ] # 4 or (9 - 1)/2 or (3 x 1) + 1 = tpo for 3 x 3 8 4 12 or (25 - 1)/2 or (5 x 2) + 2 = tpo for 5 x 5 12 4 24 or (49 - 1)/2 or (7 x 3) + 3 = tpo for 7 x 7 16 4 40 or (81 - 1)/2 or (9 x 4) + 4 = tpo for 9 x 9 20 4 60 or (121 - 1)/2 or (11 x 5) + 5 = tpo for 11 x 11 24 4 84 or (169 - 1)/2 or (13 x 6) + 6 = tpo for 13 x 13 28 4 112 or (225 - 1)/2 or (15 x 7) + 7 = tpo for 15 x 15 [ note: 4/1 = 4 12/2 = 6 24/3 = 8 40/4 = 10 60/5 = 12 84/6 = 14 112/7 = 16 and (1 x 2) + 2 = 4 (2 x 2) + 2 = 6 (2 x 3) + 2 = 8 and so on and (3 - 1)/2 = 1 (5 - 1)/2 = 2 (7 - 1)/2 = 3 (9 - 1)/2 = 4 and so on and 9 - 1 = 1 x 8 25 - 1 = 3 x 8 49 - 1 = 6 x 8 81 - 1 = 10 x 8 121 - 1 = 15 x 8 169 - 1 = 21 x 8 225 - 1 = 28 x 8 and so on ] # And where am I going with this? Wherever it takes me. - As you can see, 105 is an important number. It is what I call a node number. Its being divisible by 3, and by 5, and by 7, is what allows 101 and 103 and 107 and 109 to each be a number divisible only by itself and 1. 15 is a node number. The next such number is 945, if one goes by a calculator; but it comes after 29's power has kicked in. At 105, 11's power has not yet kicked in. If 5 and 9 are ignored, 231 becomes a node number in a different family of node numbers; but any number whose final digit is not "5" is of less interest because 3 divides into an odd number every six numbers, and so would divide into 237; and 5, of course, divides into 235. Actually, what I am trying to do is uncover patterns I had missed on earlier searches. - Brian A. J. Salchert
Thinking Lizard
About Me
- brian (baj) salchert
- Rhodingeedaddee is my node blog. See my other blogs and recent posts.
Tuesday, February 19, 2008
sw00816math-about.subtracting.squares
Subscribe to:
Post Comments (Atom)
No comments:
Post a Comment