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A049502 Major index of n, 2nd definition. 10
0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 2, 0, 1, 0, 0, 0, 1, 2, 2, 3, 4, 3, 3, 0, 1, 2, 2, 0, 1, 0, 0, 0, 1, 2, 2, 3, 4, 3, 3, 4, 5, 6, 6, 4, 5, 4, 4, 0, 1, 2, 2, 3, 4, 3, 3, 0, 1, 2, 2, 0, 1, 0, 0, 0, 1, 2, 2, 3, 4, 3, 3, 4, 5, 6, 6, 4, 5, 4, 4, 5, 6, 7, 7, 8, 9, 8, 8, 5, 6, 7, 7, 5, 6, 5, 5, 0, 1, 2, 2, 3, 4, 3, 3, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,11

COMMENTS

a(A023758(n)) = 0; a(A101082(n)) > 0. - Reinhard Zumkeller, Jun 17 2015

REFERENCES

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

LINKS

Lars Blomberg, Table of n, a(n) for n = 0..10000

FORMULA

Write n in binary; add positions where there are 1's followed by 0's, counting from right.

EXAMPLE

83 = 1010011 has 1's followed by 0's in positions 2 and 5 (reading from the right), so a(83)=7.

MAPLE

A049502 := proc(n)

    local a, ndgs, p ;

    a := 0 ;

    ndgs := convert(n, base, 2) ;

    for p from 1 to nops(ndgs)-1 do

        if op(p, ndgs)- op(p+1, ndgs) = 1 then

            a := a+p ;

        end if;

    end do:

    a ;

end proc: # R. J. Mathar, Oct 17 2012

MATHEMATICA

Table[Total[Flatten[Position[Partition[Reverse[IntegerDigits[n, 2]], 2, 1], _?(#=={1, 0}&)]]], {n, 0, 110}] (* Harvey P. Dale, Oct 05 2013 *)

PROG

(Haskell)

a049502 = f 0 1 where

   f m i x = if x <= 4

                then m else f (if mod x 4 == 1

                                  then m + i else m) (i + 1) $ div x 2

-- Reinhard Zumkeller, Jun 17 2015

(Python)

def m(n):

    x=bin(int(n))[2:][::-1]

    s=0

    for i in range(1, len(x)):

        if x[i-1]=="1" and x[i]=="0":

            s+=i

    return s

for i in range(0, 10001):

    print str(i)+" "+str(m(i)) \\ Indranil Ghosh, Dec 22 2016

CROSSREFS

Cf. A049501, A037800.

Cf. A023758, A101082.

Sequence in context: A004586 A116511 A248211 * A242284 A306595 A292592

Adjacent sequences:  A049499 A049500 A049501 * A049503 A049504 A049505

KEYWORD

nonn,base,nice,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Erich Friedman, Feb 19 2000

STATUS

approved

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Last modified December 9 19:51 EST 2019. Contains 329879 sequences. (Running on oeis4.)