A049502 Major index of n, 2nd definition.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• base
• nice
• easy

Comments

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

Examples

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

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

Crossrefs

Cf. A049501, A037800.

Cf. A023758, A101082.

Programs

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

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 *)
Table[Total[SequencePosition[Reverse[IntegerDigits[n,2]],{1,0}][[All,1]]],{n,0,120}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 26 2020 *)

PARI

a(n)=if(n<5, return(0)); sum(i=0,exponent(n)-1, (bittest(n,i) && !bittest(n,i+1))*(i+1)) \\ Charles R Greathouse IV, Jan 30 2023

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(101):
    print(str(i)+" "+str(m(i))) # Indranil Ghosh, Dec 22 2016

Formula

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

Extensions

More terms from Erich Friedman, Feb 19 2000