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Casio also makes label printers which can be used with rolls of paper for the Casio BASIC calculators. [2] Programs, variables, data, and other items can be exchanged from one calculator to another (via SB-62 cable) and to and from a computer (via USB cable). All new models of Casio graphing calculators have both ports and include both cables.
If the number subtracted was the i th Fibonacci number F(i), put a 1 in place i − 2 in the code word (counting the left most digit as place 0). Repeat the previous steps, substituting the remainder for N, until a remainder of 0 is reached. Place an additional 1 after the rightmost digit in the code word.
A repfigit, or Keith number, is an integer such that, when its digits start a Fibonacci sequence with that number of digits, the original number is eventually reached. An example is 47, because the Fibonacci sequence starting with 4 and 7 (4, 7, 11, 18, 29, 47) reaches 47.
With the exceptions of 1, 8 and 144 (F 1 = F 2, F 6 and F 12) every Fibonacci number has a prime factor that is not a factor of any smaller Fibonacci number (Carmichael's theorem). [57] As a result, 8 and 144 ( F 6 and F 12 ) are the only Fibonacci numbers that are the product of other Fibonacci numbers.
For Fibonacci numbers starting with F 1 = 0 and F 2 = 1 and with each succeeding Fibonacci number being the sum of the preceding two, one can generate a sequence of Pythagorean triples starting from (a 3, b 3, c 3) = (4, 3, 5) via
The maximum period of lagged Fibonacci generators depends on the binary operation . If addition or subtraction is used, the maximum period is (2 k − 1) × 2 M−1. If multiplication is used, the maximum period is (2 k − 1) × 2 M−3, or 1/4 of period of the additive case. If bitwise xor is used, the maximum period is 2 k − 1.
Fibonacci search has an average- and worst-case complexity of O(log n) (see Big O notation). The Fibonacci sequence has the property that a number is the sum of its two predecessors. Therefore the sequence can be computed by repeated addition. The ratio of two consecutive numbers approaches the Golden ratio, 1.618... Binary search works by ...
For instance, 1/3+1/4 = 7/12, so a notation like would represent the number that would now more commonly be written as the mixed number , or simply the improper fraction . Notation of this form can be distinguished from sequences of numerators and denominators sharing a fraction bar by the visible break in the bar.