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

0,11

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 *)
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 *)

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

Crossrefs

Cf. A049501, A037800.

Cf. A023758, A101082.

Sequence in context: A004586 A116511 A248211 * A242284 A333624 A306595

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