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1, 2, -3, 4, 5, -6, -7, 8, 9, 10, -11, -12, 13, -14, -15, 16, 17, 18, -19, 20, 21, -22, -23, -24, 25, 26, -27, -28, 29, -30, -31, 32, 33, 34, -35, 36, 37, -38, -39, 40, 41, 42, -43, -44, 45, -46, -47, -48, 49, 50, -51, 52, 53, -54, -55, -56, 57, 58, -59, -60, 61, -62, -63, 64, 65, 66, -67, 68, 69, -70, -71, 72, 73, 74, -75
(list;
graph;
refs;
listen;
history;
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internal format)
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OFFSET
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1,2
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COMMENTS
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Previous name was: Flag n when the first difference of the decimal encoding of the Gray code is negative. (With "flag" meaning negate n when the difference is negative.)
Merge A091072 with minus A091067 maintaining increasing absolute value.
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LINKS
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FORMULA
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EXAMPLE
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A003188 begins 0 1 3 2 6 7 5 4 12 13 15 14 10 11 9 ... so
A055975 begins 1 2 -1 4 1 -2 -1 8 1 2 -1 -4 1 -2 ...
Sequence 1, 2,-3, 4, 5,-6,-7, 8, 9, 10,-11,-12, 13,-14, ...
Negative terms are at positions 3,6,7,11,12,14,..., = A091067.
Positive terms are the complement, which is A091072.
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MAPLE
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isA091067 := proc(n) option remember ; if n mod 4 = 3 then RETURN(true) ; else if n mod 2 = 0 then if isA091067(n/2) then RETURN(true) ; fi ; fi ; RETURN(false) ; fi ; end: A119972 := proc(n) if isA091067(n) then -n ; else n ; fi ; end: for n from 1 to 180 do printf("%d, ", A119972(n)) ; od ; # R. J. Mathar, May 14 2007
# second Maple program:
a:= n-> numtheory[jacobi](-1, n)*n:
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MATHEMATICA
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a[n_] := n KroneckerSymbol[-1, n];
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PROG
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CROSSREFS
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KEYWORD
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easy,sign,mult
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AUTHOR
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EXTENSIONS
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New name using existing formula from Joerg Arndt, Jan 19 2023
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STATUS
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approved
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