Decomposing Fibonacci Numbers#3368
Some Fibonacci numbers are immune to zombie attack—as prime numbers, they cannot be decomposed.
Fibonacci numbers are defined by the following recurrence relations:
You will be given an indefinite number of ranges of integers, each representable as a 64-bit signed integer. For each range, report in increasing order the Fibonacci numbers within that range, as well as their base-2 logarithm and their prime factorization (the prime numbers in increasing order whose product equals the Fibonacci number). If there is no Fibonacci number in the range, report that fact.
Reminder:
The logarithm of zero is undefined, even though zero is the first Fibonacci number. Also, by definition, and have no prime factors, although both are Fibonacci numbers.
To calculate the logarithm with base , use \log_c(x) = \log(x)/\log(c), where you may use your preferred logarithm (common or natural).
The input consists of an unspecified number of lines, each containing two non-negative integers ( and ) separated by a space, given in hexadecimal format (for example, denotes the decimal value ). Each integer fits within a -bit signed integer. The input ends on end-of-file or when lo > hi.
For each range, output the range itself and the information of the Fibonacci numbers as shown in the sample output, separating each range with a blank line. Note that the base- logarithm () should be printed with six digits after the decimal point, and that the prime factors are separated by single spaces.
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