A119972 a(n) = n * A034947(n).

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

Offset

1,2

Comments

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.

Links

Table of n, a(n) for n=1..75.

Formula

a(n) = n*Kronecker(-1, n) = n * A034947(n). - Andrew Howroyd, Aug 06 2018

Example

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.

Maple

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:
seq(a(n), n=1..75);  # Alois P. Heinz, Jan 19 2023

Mathematica

a[n_] := n KroneckerSymbol[-1, n];
Array[a, 75] (* Jean-François Alcover, Apr 09 2020 *)

Prog

(PARI) a(n) = n*kronecker(-1, n); \\ Andrew Howroyd, Aug 06 2018

Crossrefs

Cf. A034947, A003188, A055975, A091067, A091072.

Sequence in context: A099570 A114142 A020725 * A131738 A199969 A303502

Adjacent sequences: A119969 A119970 A119971 * A119973 A119974 A119975

Keyword

easy,sign,mult

Author

Alford Arnold, Jun 01 2006

Extensions

More terms from R. J. Mathar, May 14 2007

Keyword:mult added by Andrew Howroyd, Aug 06 2018

New name using existing formula from Joerg Arndt, Jan 19 2023

Status

approved