What is the Fibonacci code?
813243
a sequence of numbers in which the two previous numbers add to give you the third.\n1,1,2,3,5,8,13...ect\nOne plus one is two.\nOne plus two is three\nTwo plus three is five\nFive plus three is Eight...\n\nIt 's being found increasingly in nature now as well.
673019
The golden ratio is approximately 1.618...\nFibonacci numbers are 1,1,2,3,5,8,13,21,44...\nOkay, now the relationship.\n1/1 is smaller than the golden ratio.\n2/1 is bigger than the golden ratio.\n3/2 is smaller than the golden ratio.\n5/3 is bigger than the golden ratio.\n8/5 is smaller than the golden ratio.\nand so on...
1142175
One property of fibonacci series is the following\n Take two consecutive fibonacci numbers and apply to them the euclidean division algorithm.\nThen they will get the maximum number of steps( or the maximum number of divisions).\n So a computer will require more time for division of big numbers if you use euclidean division algorithm.
1071317
There are exactly 343 combinations.  I can list them all, but others have already cluttered this thread quite well on their own.  ^.^\n\nYou can think of the solution set as a series of tiered combinations.  These would start with those sets beginning with a $50 bill, which can contain up to 2 x $50,  2 x $20, 5 x $10, etc. which I believe someone has started already in this thread.  Or group them as pairs, triplets, etc. with the equation 50j+20k+10l+5m+1n=100, which may be a bit easier for calculations.  Or a convergent series, where A=(ways to form $5), B=(ways to form $10, including A-sets), etc.  With any method, find the different combinations for each set, then add them all up.\n\nDoing this is still tedious and prone to mistakes, and thus probably not much of an improvement over manually listing all of the combinations one by one.  It can also quickly become an insane exercise for larger values (for example, add the $2 bill, or find change for $200, or even worse).  So instead of trying to think this problem through mathematically, I found it much easier to think it through as a programming problem.  It lends itself very readily to a simple recursive subroutine using the following pseudocode:\n\nmake an empty stack\nset total combinations to 0\ncall CheckCurrency\nprint total combinations found\n\nrecursive subroutine CheckCurrency\n- if total currency in stack = 100\n- - add 1 to the total combinations\n- - (optional: display stack contents)\n- - end recursion\n- if total currency in stack > 100\n- - end recursion\n- if total currency in stack < 100, then\n- - for each valid denomination (50,20,10,5,1)\n- - - if the denomination < = smallest denomination in the stack\n- - - - push it to the stack\n- - - - call CheckCurrency\n- - - - pop it from the stack\nend of subroutine\n\nThis required only a few minutes to design, another few minutes to code, another few minutes to debug, less than 2 seconds to run, and has the wonderful bonus of being able to display every single combination if desired.  It would also be trivial to modify it so that, for example, you can find all combinations if you also include the $2 bill.  (The answer is:  4562 combinations.)  Or to find all combinations totalling $200.  (The answer is: 2930 combinations.)\n\nThe line that checks if the denomination is less than or equal to the smallest denomination currently in the stack is present to avoid a common mistake:  We want the total combinations, not total permutations.  Otherwise, the stack "50 20 20 10" would be counted differently than the stacks "50 20 10 20" and "50 10 20 20", and even "10 20 20 50".  The total permutations is much, much greater, especially if you consider each bill as unique.  Five $20 dollar bills alone have 5!=120 permutations because, after all, they are all completely different $20 bills.  Imagine the number of permutations of 100 x $1 bills, and everything in between.  o.O
317856
You have asked this question before and it is not clear what you are asking for..... The code to which you refer:\n\n1-1-2-3-5-8-13-21\n\nis a well known series of numbers referred to as the Fibonacci Sequence (the sequence continues on and the numbers quoted are the first 8). In the book, these numbers, when placed in the correct sequence (above) represent, among other things, an account number. They had been randomly written (out of sequence) beside the body in the Louvre in order to disquise their true meaning.\n\nFor more on the Fibonacci Sequence see:\n\nhttp://en.wikipedia.org/wiki/Fibonacci_number
689300
Q98 = 1,1,2,3,5 \n\nP.S: Looks like the fibonacci series
1173688
You'll find plenty of interesting and relevant info. from this link. Just scroll down to Article links.\n\nhttp://www.wholesalecentralair.com/newsletters/Fibonacci_series.htm
850716
Binet's formula is correct but inconvenient, and z_o_r_r_o is simply wrong.\n\nIt is fastest to calculate in pairs, instead of singly.\n\nnot only is (F16, F17) is easily obtained from (F15, F16) by the definition of Fibonacci numbers\n\nbut, brilliantly,\n\n(F15, F16) is easily obtained from (F7, F8)\n\nbecause for example F16 = F8 * (F8 + 2 * F7) = 21 * (21 + 26) = 987, and F15 = F8 * F8 + F7 * F7 = 21^2 + 13^2 = 610.\n\nSo whatever number you want, by progressively halving the index when it is even or subtracting 1 when it is odd, you can get down to an easily looked-up Fibonacci number in LOGARITHMIC time.
402424
f+12<18  Subtract 12 from each side.\nf < 6\nThus, the solution is all numbers less than 6.\n(-infinity,6) is called interval notation.\nSet builder notation:\n{f|f<6}\nSet builder notation is always enclosed in braces {}, and always starts out with f|\nThe vertical bar is read "such that"\nThus, {f|f<6} is read "f such that f is less than 6."\nAlso, the graph is a number line with a parenthesis, ), at 6 and then shaded to the left of 6.
129538
The next number is 30651.\nIt has a recursion, a_n=a_(n-1)^2+2*a_(n-2).
846932
The x value will be (sqrt(5) - 1) / 2, or -.618, which is 1 - phi = -1 / phi, where phi is the golden ratio.  If f_n is a fibonacci number, the ratio of f_n/f_(n+1) approaches phi - 1 as n approaches infinity.  Since the terms of your sequence are of the form f_n + f_(n+1)*x, they would approach f_n + f_(n+1)*(-f_n/f_(n+1)) = f_n - f_n = 0, a convergence.
551038
http://abstractvb.com/code.asp?F=1&P=1&A=1032
268949
It's just like the decimal system, only based on the number 2 instead of the number 10..........\n\n1  10  100  1000  10000  100000  1000000  etc... - Decimal\n\n1  2  4  8  16  32  64  128  256  512  1024  etc.. - Binary
270029
There are of course good ways and bad ways of doing this.  The best way involves using a search tree like DFS and then pruning.  Instead of showing you something this complex (since I am unsure of your level of understanding) I will show you a common simple algorithm.  I will leave the code up to you, here is the psuedo-code:\n\n----------------------------------------------------\nALGORITHM JohnsonTrotter(n)\n//input: positive integer n\n//output: a list of all permutations of (1...n)\n\ninitialize the first permutation with (1,2...n) and with a second correspoing list ('L','L',...,'L').\n\n//Definition: mobile integer = if the corresponding letter is L \n//and the left adjacent number is smaller or vise versa.\n \nwhile there exists a mobile integer k do\n     find the largest integer K\n     swap K and the adjacent integer (left one if L) right otherwise\n     reverse the direction of all integers that are larger than k\nend do while\n----------------------------------------------------\nthis is really a simple algorithm to follow and to code, I am working off memmory here so it may not be the exact terms used but the algorithm is 100% I assure you.  Hope this helps and have fun.
994598
I'm trying to work on this.  So you are saying you have something like the following:\n\n1²  4²7²6³5  5²i  b15²1²4²i\n\nAnd you are trying to figure out what the code means.  I've been trying some basic things like assuming a=1, b=2, etc. but nothing is working.  Can you give us any more hints like where you got the code from, whether it was for a certain class, etc.?\n\n-----\n\nEdit:  I figured it out!  It says "I LOVE MY FAMILY"\n\nFirst, I think you meant to put a six (6) where you have b.\n\n1²  4²7²6³5  5²i  615²1²4²i\n\nNow use the grid I created below:\nhttp://img108.imageshack.us/img108/3888/codegrid1xn.gif\n\nFind the digit by going across the columns, then go down to the appropriate power.  If there is no power it is the letter in the first row.  If it is squared (²) then use the second row.  If it is cubed (³) it will be in the third row.  Y is a special case and is i.  I don't know what Z is... it might be i², ii, v or x but we don't know without an example.\n\nAnyway, using the diagram you have:\n1²  = I\n\n4² = L\n7² = O\n6³ = V\n5 =E\n\n5² = M\ni = Y\n\n6 = F\n1 = A\n5² = M\n1²= I\n4² = L\ni = Y\n\nThe answer is: "I LOVE MY FAMILY!"
924398
practically everywhere:\nfibonaci numbers in nature for eg
590621
It looks like geek code to me.\n\nhttp://www.google.com/search?q=%22geek+code%22