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A244331
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Number of binary digits in the high-water marks of the terms of the continued fraction of the base-2 Champernowne constant.
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3
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0, 1, 3, 9, 23, 53, 115, 241, 495, 1005, 2027, 4073, 8167, 16357, 32739, 65505, 131039, 262109, 524251, 1048537, 2097111, 4194261, 8388563, 16777169
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OFFSET
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1,3
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COMMENTS
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LINKS
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FORMULA
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It appears that for n >= 4, a(n) = 2^n - 2*n + 1 = A183155(n-1).
Also it appears that if we define NCD(N) = (Sum_{m=1..N} m*2^(m-1)) - N, then for n >= 4, a(n) = NCD(n) - 2*NCD(n-1) - 3*n + 4.
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PROG
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(Ruby) puts (4..24).collect{|n| 2**n-2*n+1}
(Ruby) puts (4..24).collect {|n| (1..n).inject(0) {|sum, m| sum+m*2**(m-1)}-n-2*((1..(n-1)).inject(0) {|sum1, m1| sum1+m1*2**(m1-1)}-(n-1))-3*n+4}
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CROSSREFS
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KEYWORD
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base,nonn,more
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AUTHOR
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STATUS
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approved
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