

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
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OFFSET

0,7


REFERENCES

D. M. Bressoud, Proofs and Confirmations, Camb. Univ. Press, 1999; cf. p. 89.


LINKS

J. Stauduhar, Table of n, a(n) for n = 0..10000


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}] (* JeanFrançois 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 *)


CROSSREFS

Cf. A049502.
Sequence in context: A283272 A292166 A282192 * A102564 A215703 A292712
Adjacent sequences: A049498 A049499 A049500 * A049502 A049503 A049504


KEYWORD

nonn,base,nice,easy


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from Erich Friedman, Feb 19 2000


STATUS

approved



