A049501 Major index of n, first definition.

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

Author

N. J. A. Sloane

Keywords

• nonn
• base
• nice
• easy

Examples

			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, ...
		

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

Crossrefs

Cf. A049502.

Programs

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 *)

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'.

Extensions

More terms from Erich Friedman, Feb 19 2000