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A105670
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a(1)=1 then bracketing n by powers of 2 as f(t)=2^t for f(t) < n <= f(t+1), a(n) = f(t+1) - a(n-f(t)).
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5
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1, 1, 3, 3, 7, 7, 5, 5, 15, 15, 13, 13, 9, 9, 11, 11, 31, 31, 29, 29, 25, 25, 27, 27, 17, 17, 19, 19, 23, 23, 21, 21, 63, 63, 61, 61, 57, 57, 59, 59, 49, 49, 51, 51, 55, 55, 53, 53, 33, 33, 35, 35, 39, 39, 37, 37, 47, 47, 45, 45, 41, 41, 43, 43, 127, 127, 125, 125, 121, 121, 123
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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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a(2n-1) = a(2n).
a(n) = 2*a(ceiling(n/2)) -1 + 2*t(ceiling(n/2)-1) where t(n) = A010060(n) is the Thue-Morse sequence.
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MAPLE
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ceil(log(n)/log(2)) ;
2^% ;
end proc:
option remember;
if n = 1 then
1;
else
fn := fn1/2 ;
fn1-procname(n-fn) ;
end if;
end proc:
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MATHEMATICA
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t[0] = 0; t[1] = 1; t[n_?EvenQ] := t[n] = t[n/2]; t[n_?OddQ] := t[n] = 1 - t[(n-1)/2]; a[1] = 1; a[n_?EvenQ] := a[n] = a[n - 1]; a[n_] := a[n] = 2*a[Ceiling[n/2]] - 1 + 2*t[Ceiling[n/2] - 1]; Table[a[n], {n, 1, 71}] (* Jean-François Alcover, Aug 13 2013 *)
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PROG
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(PARI) b(n, m)=if(n<2, 1, m*m^floor(log(n-1)/log(m))-b(n-m^floor(log(n-1)/log(m)), m))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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