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...

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

integers by "small" fractions Semi-Thue system – String rewriting system Thue–Morse sequence – Infinite binary sequence generated by repeated complementation...

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

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...

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...

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...

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...

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

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

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

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...

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

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

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...

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:...

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...

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....

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

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

(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...

when trailing in the shoot-out. As a remedy, he proposed using the Thue–Morse sequence to determine the kicking order. Another, more comprehensive, analysis...

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,...

"Transcendental Infinite Products Associated with the +-1 Thue-Morse Sequence" (PDF), Journal of Integer Sequences, 23: 20.8.2, arXiv:2009.02025. Borwein, Peter (2000)...

holes punched. BIP-8 Parity function Single-event upset Check digit Thue–Morse sequence Ziemer, RodgerE.; Tranter, William H. (17 March 2014). Principles...

from an intuitionistic point of view, in which he showed, using the Thue–Morse sequence, that the then-official rules (in 1929) did not exclude the possibility...