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A092412
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Fixed point of the morphism 0->11, 1->12, 2->13, 3->10, starting from a(1) = 1.
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4
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1, 2, 1, 3, 1, 2, 1, 0, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 1, 0, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 0, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 1, 0, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 0, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 1, 0, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 0
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OFFSET
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1,2
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LINKS
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FORMULA
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a(2n+1) = 1; a(2n) = a(n) + 1 mod 4.
Multiplicative with a(2^e) = (1 + e) mod 4, a(p^e) = 1 for odd prime p. - Andrew Howroyd, Aug 06 2018
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 22/15. - Amiram Eldar, Nov 29 2022
Dirichlet g.f.: zeta(s)*(3*2^s+2^(2*s+1)+2^(3*s))/(1+2^s+4^s+8^s). - Amiram Eldar, Jan 04 2023
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MATHEMATICA
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Nest[ Function[ l, {Flatten[(l /. {0 -> {1, 1}, 1 -> {1, 2}, 2 -> {1, 3}, 3 -> {1, 0}})] }], {0}, 7] (* Robert G. Wilson v, Mar 04 2005 *)
SubstitutionSystem[{0 -> {1, 1}, 1 -> {1, 2}, 2 -> {1, 3}, 3 -> {1, 0}}, {1}, 7] // Last (* Jean-François Alcover, Sep 20 2019 *)
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PROG
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(Python)
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CROSSREFS
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KEYWORD
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easy,mult,nonn
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AUTHOR
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STATUS
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approved
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