In mathematics, the Thue–Morse or Prouhet–Thue–Morse sequence is the binary sequence (an infinite sequence of 0s and 1s) that can be obtained by starting...

expansion 0.01101001100101101001011001101001... is given by the Prouhet–Thue–Morse sequence. That is, τ = ∑ n = 0 ∞ t n 2 n + 1 = 0.412454033640 … {\displaystyle...

fallback Thue's lemma – Representation of modular integers by "small" fractions Semi-Thue system – String rewriting system Thue–Morse sequence – Infinite...

an odd number of ones. Hence, the Thue–Morse sequence is 2-automatic. The n-th term of the period-doubling sequence d(n) (OEIS: A096268) is determined...

combinations of Dirichlet series whose coefficients are terms of the Thue-Morse sequence give rise to identities involving the Riemann Zeta function. For...

now known as Morse theory. The Morse–Palais lemma, one of the key results in Morse theory, is named after him, as is the Thue–Morse sequence, an infinite...

logarithmic space. Apéry's constant can be represented in terms of the Thue-Morse sequence ( t n ) n ≥ 0 {\displaystyle (t_{n})_{n\geq 0}} , as follows: ∑ n...

curve that is generated if an automaton is programmed with a sequence. If the Thue–Morse sequence members are used in order to select program states: If t...

"Thue-Morse Sequence". mathworld.wolfram.com. Retrieved 2025-01-31. The Thue-Morse sequence, also called the Morse-Thue sequence or Prouhet-Thue-Morse...

Recamán's sequence Regular paperfolding sequence Rudin–Shapiro sequence Semiperfect numbers Semiprime numbers Superperfect numbers Triangular numbers Thue–Morse...

positions of the zero values in the Thue–Morse sequence, and for this reason they have also been called the Thue–Morse set. Non-negative integers that are...

obtained by taking the first difference of the Thue–Morse sequence. That is, from the Thue–Morse sequence 0 , 1 , 1 , 0 , 1 , 0 , 0 , 1 , 1 , 0 , 0 , 1...

the sequence. The Thue–Morse sequence t(n) (OEIS: A010060) is the fixed point of the morphism 0 → 01, 1 → 10. It is known that the Thue–Morse sequence is...

Look-and-say sequence Thue–Morse sequence List of integer sequences Types ±1-sequence Arithmetic progression Automatic sequence Cauchy sequence Constant-recursive...

integer. The sequence of intervals within which this function is positive or negative follows the same pattern as the Thue–Morse sequence. The Rvachëv...

sequence, Fibonacci word, Kolakoski sequence, regular paperfolding sequence, Rudin–Shapiro sequence, and Thue–Morse sequence. On most operating systems, including...

power of two 2i in this sequence is at position 2i − 1. Gould's sequence, the sequence of its exponents, and the Thue–Morse sequence are all self-similar:...

subsequence) that appears does so infinitely often, such as the Thue–Morse sequence or a Sturmian word This disambiguation page lists mathematics articles...

Stem-and-leaf display Function definition Sudoku (solve) Taxicab numbers Thue–Morse sequence Tic-tac-toe (noughts and crosses) Tower of Hanoi (solve) Trigonometric...

is a list of notable integer sequences with links to their entries in the On-Line Encyclopedia of Integer Sequences. OEIS core sequences Index to OEIS...

triangles. The entries of the diagonal matrix are values from Gould's sequence, with the minus signs distributed like the ones in Thue–Morse sequence....

The odious numbers give the positions of the nonzero values in the Thue–Morse sequence. Every power of two is odious, because its binary expansion has only...

Maynard Keynes publishes A Treatise on Probability. Marston Morse applies the Thue–Morse sequence to differential geometry. Emmy Noether publishes Idealtheorie...

given. Thue-Morse Sequence On-Line Encyclopedia of Integer Sequences: OEIS sequence A002260 (Triangle T(n,k) = k for k = 1..n) OEIS sequence A004736...

zero for evil numbers and one for odious numbers. The Thue–Morse sequence, an infinite sequence of 0's and 1's, has a 0 in position i when i is evil,...

11010011001011010010110011010011...; the digits are given by the Thue–Morse sequence, which does not repeat. A more far-reaching generalization addresses...

Life of the Hon. Henry Cavendish. Eugène Prouhet first applies the Thue–Morse sequence to number theory. Bernhard Riemann provides a proof of Green's theorem...

(2013). "On Rational Approximation of the Binary Thue-Morse-Mahler Number". Journal of Integer Sequences. 16 (13.2.3). Cuyt et al. 2008, p. 185. Cuyt et...

produces his first theories on Markov chain processes. Axel Thue uses the Thue–Morse sequence to found the study of combinatorics on words. September –...

Fibonacci word is (5 + √5)/2 ≈ 3.618. The critical exponent of the Thue–Morse sequence is 2. The word contains arbitrarily long squares, but in any factor...