%I #33 Jan 30 2023 12:44:07
%S 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,
%T 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,
%U 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
%N Major index of n, 2nd definition.
%C a(A023758(n)) = 0; a(A101082(n)) > 0. - _Reinhard Zumkeller_, Jun 17 2015
%D D. M. Bressoud, Proofs and Confirmations, Camb. Univ. Press, 1999; cf. p. 89.
%H Lars Blomberg, <a href="/A049502/b049502.txt">Table of n, a(n) for n = 0..10000</a>
%F Write n in binary; add positions where there are 1's followed by 0's, counting from right.
%e 83 = 1010011 has 1's followed by 0's in positions 2 and 5 (reading from the right), so a(83)=7.
%p A049502 := proc(n)
%p local a,ndgs,p ;
%p a := 0 ;
%p ndgs := convert(n,base,2) ;
%p for p from 1 to nops(ndgs)-1 do
%p if op(p,ndgs)- op(p+1,ndgs) = 1 then
%p a := a+p ;
%p end if;
%p end do:
%p a ;
%p end proc: # _R. J. Mathar_, Oct 17 2012
%t Table[Total[Flatten[Position[Partition[Reverse[IntegerDigits[n,2]],2,1],_?(#=={1,0}&)]]],{n,0,110}] (* _Harvey P. Dale_, Oct 05 2013 *)
%t 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 *)
%o (Haskell)
%o a049502 = f 0 1 where
%o f m i x = if x <= 4
%o then m else f (if mod x 4 == 1
%o then m + i else m) (i + 1) $ div x 2
%o -- _Reinhard Zumkeller_, Jun 17 2015
%o (Python)
%o def m(n):
%o x=bin(int(n))[2:][::-1]
%o s=0
%o for i in range(1,len(x)):
%o if x[i-1]=="1" and x[i]=="0":
%o s+=i
%o return s
%o for i in range(101):
%o print(str(i)+" "+str(m(i))) # _Indranil Ghosh_, Dec 22 2016
%o (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
%Y Cf. A049501, A037800.
%Y Cf. A023758, A101082.
%K nonn,base,nice,easy
%O 0,11
%A _N. J. A. Sloane_
%E More terms from _Erich Friedman_, Feb 19 2000