A276205 - OEIS

%I #14 Aug 29 2016 18:35:26

%S 0,0,0,1,0,0,2,0,0,0,1,2,1,3,0,0,0,4,0,1,2,2,3,1,4,0,0,1,0,0,0,5,3,0,

%T 7,1,0,4,2,4,2,3,5,1,1,4,1,3,0,0,0,1,0,0,2,0,0,0,9,2,8,10,0,4,0,0,0,2,

%U 1,7,13,4,12,4,6,7,4,4,2,0,10,2,2,1,3,1,0,0,0,12,0,9,1,0,5,2,1,17,0,3,5,0,1,1,0,0,8,3,0,0,0,15,12,9,10,11,1,5

%N a(0) = a(2) = a(3) = 0. For n>2 a(n) is the smallest nonnegative integer such that there is no arithmetic progression j,k,m,n (of length 4) such that a(j)+a(k)+a(m) = a(n).

%C This sequence, unlike A276204 (defined similarly) is seemingly irregular.

%C a(n) <= n/3. - _Robert Israel_, Aug 24 2016

%C The graph (and the definition) are reminiscent of A229037. - _N. J. A. Sloane_, Aug 29 2016

%H Michal Urbanski, <a href="/A276205/b276205.txt">Table of n, a(n) for n = 0..49999</a>

%e For n = 6 we have that:

%e a(6)>0, because a(0)+a(2)+a(4)=0 and 0,2,4,6 is an arithmetic progression.

%e a(6)>1, because a(3)+a(4)+a(5)=1 and 3,4,5,6 is an arithmetic progression.

%e there is no such arithmetic progression j,k,m,6 that a(j)+a(k)+a(m)=2, so a(6) = 2.

%p for i from 0 to 2 do A[i]:= 0 od:

%p for n from 3 to 200 do

%p   Forbid:= {seq(A[n-d]+A[n-2*d]+A[n-3*d],d=1..floor(n/3))};

%p   A[n]:= min({$0..max(Forbid)+1} minus Forbid)

%p od:

%p seq(A[i],i=0..200); # _Robert Israel_, Aug 24 2016

%Y Cf. A276204 (length 3), A276206 (length 5), A276207 (any length).

%Y Cf. also A229037.

%K nonn,look

%O 0,7

%A _Michal Urbanski_, Aug 24 2016