%I #4 Sep 02 2017 14:18:54

%S 1,0,0,1,0,1,0,0,2,1,0,0,2,1,0,1,0,0,0,3,2,1,0,1,0,0,0,3,2,1,0,0,2,1,

%T 0,1,0,1,0,0,0,0,4,3,2,1,0,0,2,1,0,1,0,1,0,0,0,0,4,3,2,1,0,1,0,0,0,3,

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

%N a(n) = A123249(n) - 2*n.

%C Conjecture: For k > 1, the smallest n such that a(n) = k is A123720(k) = 2^k + 2^(k-1) - k. Confirmed for k <= 22.

%H B. M. Abrego, S. Fernandez-Merchant, B. Llano, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Abrego/abrego2.html">An Inequality for Macaulay Functions</a>, J. Int. Seq. 14 (2011) # 11.7.4

%o (PARI) {m=105;w=vector(3*m);print1(a=1,",");for(n=2,m,k=n;while(w[k],k++);a=n+k;print1(a-2*n,",");w[a]=1)}

%Y Cf. A123249, A123720.

%K nonn

%O 1,9

%A _Klaus Brockhaus_, Oct 09 2006