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 A141612 Write down 0,1,2,3,...n each in binary. Total up the number of 1's in each bit-position (total number of 1's in 1's position, total number of 1's in 2's position, total number of 1's in 4's position, etc.). a(n) = the number of such totals that each do not equal any other such total. 1
 0, 1, 0, 0, 1, 1, 0, 0, 1, 2, 2, 0, 0, 1, 0, 0, 1, 2, 1, 1, 3, 3, 2, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 2, 1, 1, 2, 2, 1, 1, 3, 4, 4, 2, 2, 3, 2, 0, 0, 1, 0, 0, 2, 2, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 2, 1, 1, 2, 2, 1, 1, 2, 3, 3, 1, 1, 2, 1, 1, 3, 4, 3, 3, 5, 5, 4, 2, 2, 3, 3, 2, 2, 3, 2, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,10 LINKS EXAMPLE For n= 9, we have (with leading zeros written) 0 through 9 in binary: 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 The number of 1's in the ones position (the rightmost position) is 5. The number of 1's in the 2's position (second position from the right) is 4. The number of 1's in the 4's position is 4. The number of 1's in the 8's position (the leftmost position here) is 2. Now, the total 4 occurs twice. But the total 2 occurs once, as does the total 5. Since two totals occur once each, then a(9) = 2. MAPLE A070939 := proc(n) max(1, ilog2(n)+1) ; end: A141612aux := proc(L, c) local a, i ; a := 0 ; for i in L do a := a+1-min(1, abs(i-c)) ; od; a ; end: A141612 := proc(n) local a, k, p, bds, i; if n = 0 then RETURN(0) ; fi; a := [seq(0, i=1..A070939(n))]; for k from 0 to n do bds := convert(k, base, 2) ; for p from 1 to nops(bds) do a := subsop( p=op(p, a)+op(p, bds), a) ; od: od: bds := 0 ; for i in a do if A141612aux(a, i) = 1 then bds := bds+1; fi; od; bds; end: for n from 0 to 120 do printf("%d, ", A141612(n)) ; od: # R. J. Mathar, Sep 12 2008 CROSSREFS Sequence in context: A058190 A055736 A006997 * A316342 A297814 A298177 Adjacent sequences:  A141609 A141610 A141611 * A141613 A141614 A141615 KEYWORD nonn,base AUTHOR Leroy Quet, Aug 22 2008 EXTENSIONS Extended by R. J. Mathar, Sep 12 2008 STATUS approved

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Last modified April 1 20:21 EDT 2020. Contains 333168 sequences. (Running on oeis4.)