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A095276
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Length of n-th run of identical symbols in A095076 and A095111.
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4
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1, 3, 1, 1, 2, 1, 3, 2, 3, 1, 1, 3, 3, 1, 1, 2, 1, 3, 1, 1, 3, 1, 1, 2, 1, 3, 2, 3, 1, 1, 2, 1, 3, 1, 1, 2, 1, 3, 2, 3, 1, 1, 3, 3, 1, 1, 2, 1, 3, 2, 3, 1, 1, 2, 1, 3, 2, 3, 1, 1, 3, 3, 1, 1, 2, 1, 3, 1, 1, 3, 1, 1, 2, 1, 3, 2, 3, 1, 1, 3, 3, 1, 1, 2, 1, 3, 2, 3, 1, 1, 3, 3, 1, 1, 2, 1, 3, 1, 1, 3, 1, 1
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OFFSET
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1,2
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COMMENTS
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Conjecture: it appears that the asymptotic frequencies of terms 1, 2 and 3 are 1/2, 1/(2*phi^2) and 1/(2*phi) respectively, where phi = (1+sqrt(5))/2 is the golden ratio. - Vladimir Reshetnikov, Mar 17 2022
For a proof of this conjecture see my link to a095276.pdf. - Michel Dekking, Jun 25 2024
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LINKS
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FORMULA
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(a(n)) is a morphic sequence. Let y = GDAEABFA... be the unique fixed point of the morphism rho given by rho(A) = B, rho(B) =C, rho(C) = F, rho(D) = EA, rho(E) = FA, rho(F) = GA, rho(G) = GDA on the alphabet {A,B,C,D,E,F,G}. Then (a(n+1)) is the image of y under the morphism A->11, B->21, C->32, D->23, E->33, F->3113, G->311213. - Michel Dekking, Jun 25 2024
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MATHEMATICA
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Length /@ Split[Mod[DigitCount[Select[Range[0, 1500], BitAnd[#, 2 #] == 0 &], 2, 1], 2]] (* Amiram Eldar, Feb 07 2023 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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