%I #19 May 14 2024 07:57:01

%S 0,2,1,-3,5,-5,7,-7,9,-9,11,-11,13,-13,15,-15,17,-17,19,-19,21,-21,23,

%T -23,25,-25,27,-27,29,-29,31,-31,33,-33,35,-35,37,-37,39,-39,41,-41,

%U 43,-43,45,-45,47,-47,49,-49,51,-51

%N a(1) = 0; thereafter a(n) is the smallest number (in absolute value) not yet in the sequence such that the arithmetic mean of the first n terms a(1), a(2), ..., a(n) is an integer. Preference is given to positive values of a(n).

%H Robert Israel, <a href="/A296064/b296064.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-1,1,1).

%F From _Robert Israel_, Dec 26 2017: (Start)

%F a(n) = a(n-3)+a(n-2)-a(n-1) for n >= 7.

%F G.f.: (2+3*x-4*x^2-x^3+2*x^4)*x^2/((1-x)*(x+1)^2). (End)

%F a(n) = 1/2+(-1)^n*(1/2-n), n>=4. - _R. J. Mathar_, May 14 2024

%p 0, 2, 1, -3, seq(seq(s*i,s=[1,-1]),i=5..100,2); # _Robert Israel_, Dec 26 2017

%t Nest[Append[#, Block[{k = 1, s = 1}, While[Nand[FreeQ[#, s k], IntegerQ@ Mean[Append[#, s k]]], If[s == 1, s = -1, k++; s = 1]]; s k]] &, {0}, 51] (* _Michael De Vlieger_, Dec 12 2017 *)

%Y Cf. A296065 (partial sums), A127630.

%Y Essentially the same as A296063.

%K sign,easy

%O 1,2

%A _Enrique Navarrete_, Dec 04 2017