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 A174978 For definition see comments lines. 0
 1, 2, 1, 5, 2, 2, 1, 20, 2, 5, 2, 5, 2, 2, 1, 95, 2, 5, 2, 20, 2, 5, 2, 20, 2, 5, 2, 5, 2, 2, 1, 470, 2, 5, 2, 20, 2, 5, 2, 95, 2, 5, 2, 20, 2, 5, 2, 95, 2, 5, 2, 20, 2, 5, 2, 20, 2, 5, 2, 5, 2, 2, 1, 2345, 2, 5, 2, 20, 2, 5, 2, 95, 2, 5, 2, 20, 2, 5, 2, 470, 2, 5, 2, 20, 2, 5, 2, 95, 2, 5, 2, 20, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS It is easier to explain the rule of recurrence when the numbers are written as follows: 1, 2, 1, 5, 2, 2, 1, 20, 2, 5, 2, 5, 2, 2, 1, 95, 2, 5, 2, 20, 2, 5, 2, 20, 2, 5, 2, 5, 2, 2, 1, 470, 2, 5, 2, 20, 2, 5, 2, 95, 2, 5, 2, 20, 2, 5, 2, 95, 2, 5, 2, 20, 2, 5, 2, 20, 2, 5, 2, 5, 2, 2, 1, 2345, 2, 5, 2, 20, 2, 5, 2, 95, 2, 5, 2, 20, 2, 5, 2, 470, 2, 5, 2, 20, 2, 5, 2, 95, 2, 5, 2, 20, 2, 5, 2, 470, 2, 5, 2, 20, 2, 5, 2, 95, 2, 5, 2, 20, 2, 5, 2, 95, 2, 5, 2, 20, 2, 5, 2, 20, 2, 5, 2, 5, 2, 2, 1. At first a(2^(n+1)-1) = (3*5^n+5)/4 (n>=0). Let A be the sequence defined as follows: A(0)=2; W(A(0))=5; A(1)=A(0),W(A(0))=2, 5; W(A(1))=2, 20. More generally with A(n)=B(n), {3*5^n+5)/4; we define W(A(n))=B(n), (3*5^(n+1)+5)/4 and A(n+1)=A(n), W(A(n)). Here we obtain A(1)=2, 5; W(A(1))=2, 20; A(2)=2, 5, 2, 20; W(A(2))=2, 5, 2, 95; A(3)=2, 5, 2, 20, 2, 5, 2, 95; W(A(3))=2, 5, 2, 20, 2, 5, 2, 470; A(4)=2, 5, 2, 20, 2, 5, 2, 95, 2, 5, 2, 20, 2, 5, 2, 470, etc. In fact: B(1)=2; B(2)=2, 5, 2; B(3)=2, 5, 2, 20, 2, 5, 2; B(4)=2, 5, 2, 20, 2, 5, 2, 95, 2, 5, 2, 20, 2, 5, 2, etc. If we denote by <> the subsequence of a between a(2^(n+1)-1) and a(2^(n+2)-1), the subsequence of a between a(2^(n+2)-1) and a(2^(n+3)-1) is given by <>. It seems that this sequence gives the numbers of 1 in the successive sets of 1 in the sequence A174835. LINKS Table of n, a(n) for n=0..92. EXAMPLE a(1)=a(2^1-1)=(3*5^0+5)/4=2. a(3)=a(2^2-1)=(3*5+5)/4=5. a(7)=a(2^3-1)=(75+5)/4=20. a(15)=a(2^4-1)=(3*125+5)/4=380/4=95. Between 20 and 95 the subsequence of a is: 2, 5, 2, 5, 2, 2, 1. Then with the definition, the subsequence of a, between 95 and 470 is: A(2), A(2), 2, 5, 2, 5, 2, 2, 1, i.e., 2, 5, 2, 20, 2, 5, 2, 20, 2, 5, 2, 5, 2, 2, 1. CROSSREFS Cf. A174835, A174837. Sequence in context: A308698 A308569 A350073 * A110874 A010253 A065274 Adjacent sequences: A174975 A174976 A174977 * A174979 A174980 A174981 KEYWORD easy,nonn,uned AUTHOR Richard Choulet, Apr 03 2010 STATUS approved

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