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A245536
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Write n>=1 as either n=2^k-2^r with 0 <= r <= k-1, in which case a(2^k-2^r)=k-r-1, or as n=2^k-2^r+j with 2 <= r <= k-1, 1 <= j < 2^r-1, in which case a(2^k-2^r+j)=(k-r-1)*a(j).
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1
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0, 0, 1, 0, 0, 1, 2, 0, 0, 0, 0, 1, 0, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 0, 3, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 2, 2, 0, 0, 2, 3, 0, 4, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 2
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OFFSET
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1,7
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COMMENTS
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Defined by the recurrence given in A245196, taking G(n)=n (n>=0) and m=1.
Changing G from [0,1,2,3,4,...] to [1,2,3,4,5,6,...] produces A038374.
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LINKS
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MAPLE
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G:=[seq(n, n=0..30)];
m:=1;
f:=proc(n) option remember; global m, G; local k, r, j, np;
k:=1+floor(log[2](n)); np:=2^k-n;
if np=1 then r:=0; j:=0; else r:=1+floor(log[2](np-1)); j:=2^r-np; fi;
if j=0 then G[k-r-1+1]; else m*G[k-r-1+1]*f(j); fi;
end;
[seq(f(n), n=1..120)];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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