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A049501
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Major index of n, first definition.
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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,7
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REFERENCES
| D. M. Bressoud, Proofs and Confirmations, Camb. Univ. Press, 1999; cf. p. 89.
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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'.
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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, ...
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MATHEMATICA
| a[n_] := Total[ Flatten[ Position[ IntegerDigits[n, 2] //. {b___, 1, 0, c___} -> {b, 2, 3, c}, 2]]]; Table[a[n], {n, 0, 102}] (* From Jean-François Alcover, Dec 20 2011 *)
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CROSSREFS
| Cf. A049502.
Sequence in context: A124220 A110298 A144740 * A102564 A077762 A085496
Adjacent sequences: A049498 A049499 A049500 * A049502 A049503 A049504
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KEYWORD
| nonn,base,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Erich Friedman (efriedma(AT)stetson.edu), Feb 19 2000
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