
EXAMPLE

Example: 8[3]: 0,1,3,4 means {0,1,2,...,8} is covered thus: 0=0+0, 1=0+1, 2=1+1, 3=0+3, 4=0+4=1+3, 5=1+4, 6=3+3, 7=3+4, 8=4+4.
N[q]: set

3[2]: 0,1,
4[3]: 0,1,2,
5[3]: 0,1,2,
6[3]: 0,2,3,
7[4]: 0,1,2,3,
8[4]: 0,1,3,4,
9[4]: 0,1,3,4,
10[5]: 0,1,2,4,5,
11[5]: 0,1,2,4,5,
12[5]: 0,1,3,5,6,
13[5]: 0,1,3,5,6,
14[6]: 0,1,2,4,6,7,
15[6]: 0,1,2,4,6,7,
16[6]: 0,1,3,5,7,8,
17[6]: 0,1,3,5,7,8,
18[6]: 0,2,3,7,8,10,
19[7]: 0,1,2,4,6,8,9,
20[7]: 0,1,3,5,7,9,10,
21[7]: 0,1,3,5,7,9,10,
22[7]: 0,2,3,7,8,10,11,
23[8]: 0,1,2,4,6,8,10,11,
24[8]: 0,1,3,5,7,9,11,12,
25[8]: 0,1,3,5,7,9,11,12,
26[8]: 0,2,3,7,8,10,12,13,
27[8]: 0,1,3,4,9,10,12,13,
28[8]: 0,2,3,7,8,12,13,15,
29[9]: 0,1,3,5,7,9,11,13,14,
30[9]: 0,2,3,7,8,10,12,14,15,
31[9]: 0,1,3,4,9,10,12,14,15,
32[9]: 0,2,3,7,8,12,13,15,16,
a(5)=13 because we can obtain at most a total of 13 consecutive integers from a set of 5 integers by summing any two integers in the set or doubling any one; from the 5integer set {1,2,4,6,7}, we can obtain all 13 integers in the interval [2..14] as follows: 2=1+1, 3=1+2, 4=2+2, 5=1+4, 6=2+4, 7=1+6, 8=2+6, 9=2+7, 10=4+6, 11=4+7, 12=6+6, 13=6+7, 14=7+7.
a(16)=90 because we can obtain at most a total of 90 consecutive integers from a set of 16 integers by summing any two integers in the set or doubling any one: from the 16integer set {1,2,4,5,8,9,10,17,18,22,25,36,47,58,69,80}, we can obtain all 90 integers in the interval [2..91].  Jon E. Schoenfield, Jul 16 2017
