%I #10 Jan 04 2019 13:17:04
%S 0,1,3,0,4,1,7,0,8,1,2,0,3,1,6,0,7,1,10,0,2,1,5,0,6,1,9,0,10,1,4,0,5,
%T 1,8,0,9,1,12,0,4,1,7,0,8,1,11,0,12,1,6,0,7,1,10,0,11,1,14,0,6,1,9,0,
%U 10,1,13,0,14,1,8,0,9,1,12,0,13,1,16,0,8,1,11,0,12,1,15,0,16,1,10,0,11,1,14
%N a(n+1) = abs[ a(n) + (-1)^(n+1) * Sum_of_digits_of(n+1)], with a(0)=0.
%C a(4*k)=0, with k>=1
%C a(4*k-2)=1, with k>=1
%H Harvey P. Dale, <a href="/A138376/b138376.txt">Table of n, a(n) for n = 0..1000</a>
%p P:=proc(n) local a,i,k,w; a:=0; print(a); for i from 1 by 1 to n do w:=0; k:=i; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; a:=abs(a+(-1)^i*w); print(a); od; end: P(100);
%t nxt[{n_,a_}]:={n+1,Abs[a+(-1)^(n+1) Total[IntegerDigits[n+1]]]}; NestList[nxt,{0,0},100][[All,2]] (* _Harvey P. Dale_, Jan 04 2019 *)
%Y Cf. A037123.
%K easy,nonn,base
%O 0,3
%A _Paolo P. Lava_ and _Giorgio Balzarotti_, May 08 2008
%E Definition corrected by _N. J. A. Sloane_, Jan 04 2019