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A049502
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Major index of n, 2nd definition.
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10
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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
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OFFSET
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0,11
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COMMENTS
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REFERENCES
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D. M. Bressoud, Proofs and Confirmations, Camb. Univ. Press, 1999; cf. p. 89.
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LINKS
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FORMULA
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Write n in binary; add positions where there are 1's followed by 0's, counting from right.
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EXAMPLE
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83 = 1010011 has 1's followed by 0's in positions 2 and 5 (reading from the right), so a(83)=7.
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MAPLE
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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 ;
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MATHEMATICA
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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 *)
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PROG
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(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
(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):
(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
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CROSSREFS
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KEYWORD
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nonn,base,nice,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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