FANDOM


0, 1, 1, 2, 3, 5, 8, 11, 19, 2X, 47, 75, 100, 175, 275, 42X, 6X3, E11, 15E4, 2505, 3XE9, 6402, X2EE, 14701, 22X00, 37501, 5X301, 95802, 133E03, 209705, 341608, 54E111, 890719, 121E82X, 1XE0347, 310EE75, 5000300, 8110275, 11110575, 1922082X, 2X3311X3, 47551X11, 75882EE4, 101214X05, 176X979E9, 2780E0802, 432E885EE, 6XE079201, E22045800, ...

Note that dozenal is the only base such that 100 is a Fibonacci number (since 1 cannot be a base of a numeral system). 100 is indeed F10, and 10 is the square root of 100.

A Fibonacci number can end with any digit but 6, and if a Fibonacci number ends with 0, then it must end with 00.

The period of the final digit of Fibonacci number is 20, that of the final two digits is also 20 (dozenal is the largest base such that the period of the final digit of Fibonacci number is the same as that of the final two digits of Fibonacci number, if there are no Wall-Sun-Sun primes). For n >= 2, the period of the final n digits of Fibonacci number is 2*10^(n-1). (2 followed by n-1 zeros, which is an n-digit number 200...000)

Since 175 and 100 are two consecutive Fibonacci numbers, the golden ratio (=(-1+sqrt(5))/2 = 1.74EE6772802X...) is very close to 175/100 = 1.75, and thus very close to 175%

n F(n+1) F(n) F(n+1)/F(n)
1 1 1 1
2 2 1 2
3 3 2 1.6
4 5 3 1.8
5 8 5 1.724972
6 11 8 1.76
7 19 11 1.747475
8 2X 19 1.75186X
9 47 2X 1.74E364
X 75 47 1.750275
E 100 75 1.74EX47
10 175 100 1.75
11 275 175 1.74EE47
12 42X 275 1.74EE75
13 6X3 42X 1.74EE64
14 E11 6X3 1.74EE69