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 A073059 a(n) = (1/2)*(A073504(n+1) - A073504(n)). 4
 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Let m be any fixed positive integer and let Fr(m,n) := 3*Sum_{k = 1..n} A073504(k) - n^2 + m*n. Then Fr(m,n) allows us to generate fractal sequences, i.e., there is an integer B(m) such that the graph for Fr(n,m) is fractal-like for 1 <= n <= B(m). B(m) depends on the parity of m: B(2*p+1) = (5/3)*(4^p - 1) and B(2*p) =(2/3)*(4^p - 1). [Formula for Fr(m,n) corrected by Petros Hadjicostas, Oct 21 2019] LINKS Antti Karttunen, Table of n, a(n) for n = 1..16384 B. Cloitre, Graph of Fr(n,4) for 1 <= n <= B(4) B. Cloitre, Graph of Fr(n,6) for 1 <= n <= B(6) B. Cloitre, Graph of Fr(n,8) for 1 <= n <= B(8) B. Cloitre, Graph of Fr(n,5) for 1 <= n <= B(5) B. Cloitre, Graph of Fr(n,7) for 1 <= n <= B(7) B. Cloitre, Graph of Fr(n,9) for 1 <= n <= B(9) FORMULA a(4*k+3) = 1, a(4*k+2) = a(4*k+4) = 0, a(16*k+13) = 1, ... A073504(n) = Sum_{k = 1..n} a(k) is asymptotic to 2*n/3. a(2*n) = 0, a(4*n+3) = 1, a(4*n+1) = a(n). - Ralf Stephan, Dec 11 2004 PROG (PARI) \\ To generate graphs: for(n = 1, taille, u1=1; u2=n; while((u2!=u1)||((u2%2)==1), u3=u2; u2=floor(u2/2)+fl oor(u1/2); u1=u3; ); b[n]=u2; ) fr(m, k)=(3*sum(i=1, k, b[i]))-k^2+m*k; bound(m)=if((m%2)==1, p=(m-1)/2; 5/3*(4^p-1), 2/3*(4^(m/2)-1)); m=5; fractal=vector(bound(m)); for(i=1, bound(m), fractal[i]=fr(m, i); ); Mm=vecmax(fractal) indices=vector(bound(m)); for(i=1, bound(m), indices[i]=i); psplothraw(indices, fractal, 1); (PARI) A073059(n) = if(1==n, 0, if(!(n%2), 0, if(3==(n%4), 1, A073059((n-1)/4)))); \\ Antti Karttunen, Oct 09 2018, after Ralf Stephan's Dec 11 2004 formula (PARI) up_to = 10000; A073504list(up_to) = { my(v=vector(up_to)); for(n=1, up_to, u1=1; u2=n; while((u2!=u1)||((u2%2) == 1), u3=u2; u2=(u2\2)+(u1\2); u1=u3); v[n]=u2); (v); }; v073504 = A073504list(up_to); A073504(n) = v073504[n]; A073059(n) = (1/2)*(A073504(n+1)-A073504(n)); \\ Antti Karttunen, Nov 27 2018, after code sent by Benoit Cloitre (personal communication), implementing the original definition CROSSREFS Not the same as the period-doubling sequence A096268! Cf. A073504 and A071992 (curiously A071992 presents the same fractal aspects as Fr(n, m)). Cf. A098725. Sequence in context: A288707 A079261 A285495 * A288173 A221150 A288997 Adjacent sequences:  A073056 A073057 A073058 * A073060 A073061 A073062 KEYWORD nonn AUTHOR Benoit Cloitre and Boris Gourevitch (boris(AT)pi314.net), Aug 16 2002 EXTENSIONS Erroneous formula removed by Antti Karttunen, Oct 09 2018 STATUS approved

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Last modified June 2 14:21 EDT 2020. Contains 334787 sequences. (Running on oeis4.)