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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

Table of n, a(n) for n=0..104.

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.)