## Saturday, May 16, 2015

### More NERDY Numbers - The Tribonacci and Tridecanacci sequences.

 The Tribonacci Sequence is similar to the Fibonacci sequence, except we add the three previous terms.  Mathematically it is described as:  a(0) = a(1) = 0, a(2) = 1, and when n > 2 then a(n) = a(n – 1) + a(n – 2) + a(n – 3). The decimal expansion of the inverse of 999,998,999,998,999,999 produces a sequence that show Tribonacci numbers in 6 digit chunks up to the 24th Tribonacci number. The decimal expansion of the inverse of 999,999,999,998,999,999,999,998,999,999,999,999 produces a sequence that shows Tribonacci numbers in 12 digit chunks  up to the 47th Tribonacci number. 1/999999999998999999999998999999999999 = 0. 000000000000 000000000000 000000000001 000000000001 000000000002 000000000004 000000000007 000000000013 000000000024 000000000044 000000000081 000000000149 000000000274 000000000504 000000000927 000000001705 000000003136 000000005768 000000010609 000000019513 000000035890 000000066012 000000121415 000000223317 000000410744 000000755476 000001389537 000002555757 000004700770 000008646064 000015902591 000029249425 000053798080 000098950096 000181997601 000334745777 000615693474 001132436852 002082876103 003831006429 007046319384 012960201916 023837527729 043844049029 080641778674 148323355432 272809183135 501774317241 …

After the Tribonacci sequence there are the Tetranacci, Pentanacci, Hexanacci, Heptanacci, Octanacci, Nonanacci, Decanacci, Undecanacci, Dodecanacci, and Tridecanacci sequence.  I’m going to skip ahead to my daughter’s personal favorite (she really, really, really likes the number 13).

 Tridecanacci Sequence is similar to the Fibonacci sequence, except now we will add the 13 previous Tridecanacci numbers to get the next term:  a(0) = a(1) = a(2) = a(3) = a(4) = a(5) = a(6) = a(7) = a(8) = a(9) = a(10) = a(11) = 0, a(12) = 1, and when n > 12 then a(n) = a(n – 1) + a(n – 2) + a(n – 3) + a(n – 4) + a(n – 5) + a(n – 6) + a(n – 7) + a(n – 8) + a(n – 9) + a(n -10) + a(n – 11) + a(n – 12) + a(n-13). 999,998,999,998,999,998,999,998,999,998,999,998,999,998,999, 998,999,998,999,998,999,998,999,998,999,999 will produce 6 digit chunks.  999,999,999,998,999,999,999,998,999,999,999,998,999,999,999, 998,999,999,999,998,999,999,999,998,999,999,999,998,999,999, 999,998,999,999,999,998,999,999,999,998,999,999,999,998,999, 999,999,998,999,999,999,999 will produce 12 digit chunks. WARNING: PLEASE DO NOT TRY THIS ON YOUR HAND HELD CALCULATOR. 1/999999999998999999999998999999999998999999999998999 99999999899999999999899999999999899999999999899999999 9998999999999998999999999998999999999998999999999999 = 0 000000000000 000000000000 000000000000 000000000000 000000000000 000000000000 000000000000 000000000000 000000000000 000000000000 000000000000 000000000000 000000000001 000000000001 000000000002 000000000004 000000000008 000000000016 000000000032 000000000064 000000000128 000000000256 000000000512 000000001024 000000002048 000000004096 000000008191 000000016381 000000032760 000000065516 000000131024 000000262032 000000524032 000001048000 000002095872 000004191488 000008382464 000016763904 000033525760 000067047424 000134086657 000268156933 000536281106 001072496696 002144862368 004289462704 008578401376 017155754752 034309413632 068614635776 137220889088 274425014272 …

OK now!  Technology is still throwing me some curve balls, but I am slowly learning how to deal with some of the issues.
I'll switch up on my next post and try to show you some different kind of NERDY numbers.

David