A276205 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).

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, 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, 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

Offset: 0

Author

Michal Urbanski, Aug 24 2016

Keywords

• nonn
• look

Comments

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

a(n) <= n/3. - Robert Israel, Aug 24 2016

The graph (and the definition) are reminiscent of A229037. - N. J. A. Sloane, Aug 29 2016

Examples

			For n = 6 we have that:
a(6)>0, because a(0)+a(2)+a(4)=0 and 0,2,4,6 is an arithmetic progression.
a(6)>1, because a(3)+a(4)+a(5)=1 and 3,4,5,6 is an arithmetic progression.
there is no such arithmetic progression j,k,m,6 that a(j)+a(k)+a(m)=2, so a(6) = 2.
		

Links

• Michal Urbanski, Table of n, a(n) for n = 0..49999

Crossrefs

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

Cf. also A229037.

Programs

Maple

for i from 0 to 2 do A[i]:= 0 od:
for n from 3 to 200 do
  Forbid:= {seq(A[n-d]+A[n-2*d]+A[n-3*d],d=1..floor(n/3))};
  A[n]:= min({$0..max(Forbid)+1} minus Forbid)
od:
seq(A[i],i=0..200); # Robert Israel, Aug 24 2016