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 A231204 If n = Sum_{i=0..m} c(i)*2^i, c(i) = 0 or 1, then a(n) = Sum_{i=0..m} (m-i)*c(i). 19
 0, 0, 0, 1, 0, 2, 1, 3, 0, 3, 2, 5, 1, 4, 3, 6, 0, 4, 3, 7, 2, 6, 5, 9, 1, 5, 4, 8, 3, 7, 6, 10, 0, 5, 4, 9, 3, 8, 7, 12, 2, 7, 6, 11, 5, 10, 9, 14, 1, 6, 5, 10, 4, 9, 8, 13, 3, 8, 7, 12, 6, 11, 10, 15, 0, 6, 5, 11, 4, 10, 9, 15, 3, 9, 8, 14, 7, 13, 12, 18, 2, 8, 7, 13, 6, 12, 11, 17, 5, 11, 10, 16, 9, 15, 14, 20, 1, 7, 6, 12 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS A literal interpretation of the binary numbers. Sum of the number of digits to the left (exclusive) of each 1 in the binary expansion of n. - Gus Wiseman, Jan 09 2023 LINKS Rémy Sigrist, Table of n, a(n) for n = 0..8192 FORMULA a(n) = A230877(n) - A000120(n). - Gus Wiseman, Jan 09 2023 EXAMPLE For n=13 we have 1101, so we add 0+1+3=4, getting a(13)=4. MAPLE f:=proc(n) local t1, m, i; t1:=convert(n, base, 2); m:=nops(t1)-1; add((m-i)*t1[i+1], i=0..m); end; # N. J. A. Sloane, Nov 08 2013 MATHEMATICA Table[Total[Join@@Position[IntegerDigits[n, 2], 1]-1], {n, 0, 100}] (* Gus Wiseman, Jan 09 2023 *) PROG (JavaScript) for (i=0; i<100; i++) { s=i.toString(2); o=0; sl=s.length; for (j=0; j

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Last modified February 22 06:21 EST 2024. Contains 370240 sequences. (Running on oeis4.)