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%I #25 Jan 19 2023 15:32:06
%S 1,2,-3,4,5,-6,-7,8,9,10,-11,-12,13,-14,-15,16,17,18,-19,20,21,-22,
%T -23,-24,25,26,-27,-28,29,-30,-31,32,33,34,-35,36,37,-38,-39,40,41,42,
%U -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
%N a(n) = n * A034947(n).
%C 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.)
%C Merge A091072 with minus A091067 maintaining increasing absolute value.
%F a(n) = n*Kronecker(-1, n) = n * A034947(n). - _Andrew Howroyd_, Aug 06 2018
%e A003188 begins 0 1 3 2 6 7 5 4 12 13 15 14 10 11 9 ... so
%e A055975 begins 1 2 -1 4 1 -2 -1 8 1 2 -1 -4 1 -2 ...
%e Sequence 1, 2,-3, 4, 5,-6,-7, 8, 9, 10,-11,-12, 13,-14, ...
%e Negative terms are at positions 3,6,7,11,12,14,..., = A091067.
%e Positive terms are the complement, which is A091072.
%p 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
%p # second Maple program:
%p a:= n-> numtheory[jacobi](-1, n)*n:
%p seq(a(n), n=1..75); # _Alois P. Heinz_, Jan 19 2023
%t a[n_] := n KroneckerSymbol[-1, n];
%t Array[a, 75] (* _Jean-François Alcover_, Apr 09 2020 *)
%o (PARI) a(n) = n*kronecker(-1, n); \\ _Andrew Howroyd_, Aug 06 2018
%Y Cf. A034947, A003188, A055975, A091067, A091072.
%K easy,sign,mult
%O 1,2
%A _Alford Arnold_, Jun 01 2006
%E More terms from _R. J. Mathar_, May 14 2007
%E Keyword:mult added by _Andrew Howroyd_, Aug 06 2018
%E New name using existing formula from _Joerg Arndt_, Jan 19 2023
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