A049502 - OEIS

%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