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A049501
Major index of n, first definition.
10
0, 0, 1, 0, 1, 1, 2, 0, 1, 1, 4, 1, 2, 2, 3, 0, 1, 1, 5, 1, 4, 4, 5, 1, 2, 2, 6, 2, 3, 3, 4, 0, 1, 1, 6, 1, 5, 5, 6, 1, 4, 4, 9, 4, 5, 5, 6, 1, 2, 2, 7, 2, 6, 6, 7, 2, 3, 3, 8, 3, 4, 4, 5, 0, 1, 1, 7, 1, 6, 6, 7, 1, 5, 5, 11, 5, 6, 6, 7, 1, 4, 4, 10, 4, 9, 9, 10, 4, 5, 5, 11, 5, 6, 6, 7, 1, 2, 2, 8, 2, 7, 7, 8
OFFSET
0,7
REFERENCES
D. M. Bressoud, Proofs and Confirmations, Camb. Univ. Press, 1999; cf. p. 89.
LINKS
FORMULA
Write n in binary; sum the positions where there is a '1' followed immediately to the right by a '0', counting the leftmost digit as position '1'.
EXAMPLE
50 = 110010 has 1's followed by 0's in positions 2 and 5 (reading from the left), so a(50)=7. At the beginning of the sequence we have 0->0, 1->0, 10->1, 11->0, 100->1, 101->1, 110->2, 111->0, 1000->1, 1001->1, 1010->1+3=4, ...
MATHEMATICA
a[n_] := Total[ Flatten[ Position[ IntegerDigits[n, 2] //. {b___, 1, 0, c___} -> {b, 2, 3, c}, 2]]]; Table[a[n], {n, 0, 102}] (* Jean-François Alcover, Dec 20 2011 *)
Table[Total[Flatten[Position[Partition[IntegerDigits[n, 2], 2, 1], {1, 0}]]], {n, 0, 110}] (* Harvey P. Dale, Nov 04 2012 *)
Table[Total[SequencePosition[IntegerDigits[n, 2], {1, 0}][[;; , 1]]], {n, 0, 110}] (* Harvey P. Dale, Feb 19 2023 *)
CROSSREFS
Cf. A049502.
Sequence in context: A283272 A292166 A282192 * A102564 A215703 A292712
KEYWORD
nonn,base,nice,easy
EXTENSIONS
More terms from Erich Friedman, Feb 19 2000
STATUS
approved