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A043261
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Sum of the binary digits of the n-th base-2 palindrome.
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1
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0, 1, 2, 2, 3, 2, 4, 2, 3, 4, 5, 2, 4, 4, 6, 2, 3, 4, 5, 4, 5, 6, 7, 2, 4, 4, 6, 4, 6, 6, 8, 2, 3, 4, 5, 4, 5, 6, 7, 4, 5, 6, 7, 6, 7, 8, 9, 2, 4, 4, 6, 4, 6, 6, 8, 4, 6, 6, 8, 6, 8, 8, 10, 2, 3, 4, 5, 4, 5, 6, 7, 4, 5, 6, 7, 6, 7, 8, 9, 4, 5, 6, 7, 6, 7, 8, 9, 6, 7, 8
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OFFSET
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1,3
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LINKS
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FORMULA
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Let b(1) = 0, b(2) = 1, otherwise b(2*n-1) = b(n-1) and b(2*n) = b(n).
Let c(1) = 0, c(2) = 1, otherwise c(2*n-1) = c(n-1)+1 and c(2*n) = c(n).
Then for n >= 2, a(2*n-1) = 2*c(2*n-1) - b(2*n-1) and a(2*n) = 2*c(2*n).
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EXAMPLE
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The fourth base-2 palindrome is 5 = 101_2, so a(4) = 1+0+1 = 2.
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MAPLE
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b:= proc(n) option remember;
procname(floor(n/2)) end proc;
b(1):= 0; b(2):= 1;
c:= proc(n) option remember;
procname(floor(n/2)) + (n mod 2) end proc;
c(1):= 0; c(2):= 1;
A043261:= n -> 2*c(n) - (n mod 2)*b(n);
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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