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The ratio of Fibonacci numbers and , each over digits, yields over significant digits of the golden ratio. The decimal expansion of the golden ratio φ {\displaystyle \varphi } [ 1 ] has been calculated to an accuracy of ten trillion ( 1 × 10 13 = 10,000,000,000,000 {\displaystyle \textstyle 1\times ...
Smallest base which is not perfect odd power (where generalized Wagstaff numbers can be factored algebraically) for which no generalized Wagstaff primes are known. 100: Centesimal: As 100=10 2, these are two decimal digits. 121: Number expressible with two undecimal digits. 125: Number expressible with three quinary digits. 128: Using as 128=2 7.
Since the conversion factor 1.609344 for miles to kilometers is close to the golden ratio, the decomposition of distance in miles into a sum of Fibonacci numbers becomes nearly the kilometer sum when the Fibonacci numbers are replaced by their successors. This method amounts to a radix 2 number register in golden ratio base φ being shifted. To ...
The above formulas for the ratio hold even for -nacci series generated from arbitrary numbers. The limit of this ratio is 2 as increases. An "infinacci" sequence, if one could be described, would after an infinite number of zeroes yield the sequence [..., 0, 0, 1,] 1, 2, 4, 8, 16, 32, …
Individual numbers in the Lucas sequence are known as Lucas numbers. Lucas numbers and Fibonacci numbers form complementary instances of Lucas sequences . The Lucas sequence has the same recursive relationship as the Fibonacci sequence, where each term is the sum of the two previous terms, but with different starting values. [ 1 ]
Ratio of a circle's circumference to its diameter. 1900 to 1600 BCE [2] Tau: 6.28318 53071 79586 47692 [3] [OEIS 2] Ratio of a circle's circumference to its radius. Equal to : 1900 to 1600 BCE [2] Square root of 2, Pythagoras constant [4]
The golden ratio (denoted or ) is ... [30] Any number for which the digits with respect to some fixed base form a Sturmian word. [31] ... Code of Conduct; Developers;
The reciprocal Fibonacci constant ψ is the sum of the reciprocals of the Fibonacci numbers: = = = + + + + + + + +. Because the ratio of successive terms tends to the reciprocal of the golden ratio, which is less than 1, the ratio test shows that the sum converges.