A049501 - OEIS

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

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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}] (* 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

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