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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 *) 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

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Last modified September 27 20:41 EDT 2023. Contains 365714 sequences. (Running on oeis4.)