The reciprocal Fibonacci constant ψ is the sum of the reciprocals of the Fibonacci numbers: ψ = ∑ k = 1 ∞ 1 F k = 1 1 + 1 1 + 1 2 + 1 3 + 1 5 + 1 8 + 1...

^{2k}}}-{\frac {\psi ^{4k}}{1-\psi ^{4k}}}\right)\!.} So the reciprocal Fibonacci constant is ∑ k = 1 ∞ 1 F k = ∑ k = 1 ∞ 1 F 2 k − 1 + ∑ k = 1 ∞ 1 F 2...

Fibonacci generator Negafibonacci NegaFibonacci coding Pisano period Reciprocal Fibonacci constant Young–Fibonacci lattice A professional association and...

"Paper Folding Constant". MathWorld. Weisstein, Eric W. "Reciprocal Fibonacci Constant". MathWorld. Weisstein, Eric W. "Feigenbaum Constant". MathWorld....

\sum _{k=1}^{\infty }1/F_{n}} is finite, and is called the reciprocal Fibonacci constant. By the Birkhoff's ergodic theorem, the limit lim n → ∞ ln ⁡...

In mathematics, the Fibonacci numbers form a sequence defined recursively by: F n = { 0 n = 0 1 n = 1 F n − 1 + F n − 2 n > 1 {\displaystyle...

non-zero triangular numbers is 2 . The reciprocal Fibonacci constant is the sum of the reciprocals of the Fibonacci numbers, which is known to be finite...

308, issue 19 (1989), pp. 539-541. S. Kato, 'Irrationality of reciprocal sums of Fibonacci numbers', Master's thesis, Keio Univ. 1996 Duverney, Daniel,...

research into extrasensory perception). In mathematics, the reciprocal Fibonacci constant, the division polynomials, and the supergolden ratio. Water...

Probability of ultimate ruin, in ruin theory Supergolden ratio Reciprocal Fibonacci constant Population Stability Index (Kullback–Leibler divergence#Symmetrised...

particle physics the stream function in fluid dynamics the reciprocal Fibonacci constant the second Chebyshev function in number theory the polygamma...

multiple of φ {\displaystyle \varphi } and a constant. The multiple and the constant are always adjacent Fibonacci numbers. This leads to another property...

many formulas in physics, and several physical constants are most naturally defined with π or its reciprocal factored out. For example, the ground state...

algorithm for Egyptian fractions is a greedy algorithm, first described by Fibonacci, for transforming rational numbers into Egyptian fractions. An Egyptian...

The number π (/paɪ/; spelled out as "pi") is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal...

The multiplicative inverse (reciprocal) of the square root of two (i.e., the square root of ⁠1/2⁠) is a widely used constant. 1 2 = 2 2 = sin ⁡ 45 ∘ = cos...

sample python implementation of a similar (16 bit taps at [16,15,13,4]) Fibonacci LFSR would be start_state = 1 << 15 | 1 lfsr = start_state period = 0...

calculated by means of a recurrence relation similar to that for the Fibonacci numbers, and both sequences of numbers grow exponentially, proportionally...

this triple is not primitive.) For Fibonacci numbers starting with F1 = 0 and F2 = 1 and with each succeeding Fibonacci number being the sum of the preceding...

theory with more consolidated theories. Integer sequence Fibonacci sequence Golden mean base Fibonacci coding Lucas sequence Padovan sequence Figurate numbers...

S2CID 126293429. Washington, L. C. (1981). "Benford's Law for Fibonacci and Lucas Numbers". The Fibonacci Quarterly. 19 (2): 175–177. Duncan, R. L. (1967). "An...

and Φ), and its reciprocal, provide an interesting pattern of continued fractions and are related to the ratios between the Fibonacci numbers and the...

integral Legendre's constant Skewes' number Bertrand's postulate Proof of Bertrand's postulate Proof that the sum of the reciprocals of the primes diverges...

exponential Carlitz polynomial (disambiguation) Maillet's determinant Reciprocal Fibonacci constant Brawley, Joel V.; Brillhart, John; Gould, Henry W. (2012), "Recollections...

digit value −1 by its reciprocal. Other ways of encoding integers that avoid consecutive 1s include Booth encoding and Fibonacci coding. There are several...

(PDF) on 2017-07-05, retrieved 2011-05-21. McDaniel, Wayne L. (1998), "Pronic Fibonacci numbers" (PDF), Fibonacci Quarterly, 36 (1): 56–59, MR 1605341....

Fibonacci applies the algebraic identity above to each these two parts, producing the expansion ⁠8/11⁠ = ⁠1/2⁠ + ⁠1/22⁠ + ⁠1/6⁠ + ⁠1/66⁠. Fibonacci describes...

integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on. In a finite...

fraction with one as its numerator, 1/n. It is the multiplicative inverse (reciprocal) of the denominator of the fraction, which must be a positive natural...

infinite product of nested radicals representing twice the reciprocal of the mathematical constant π: 2 π = 2 2 ⋅ 2 + 2 2 ⋅ 2 + 2 + 2 2 ⋯ {\displaystyle {\frac...