[seqfan] Three Sequences

[Ali Sada]

Hi everyone,

Please see the three sequences below. If they fit OEIS, I would really appreciate help with definitions and terms.

1)    

a(n) is a positive integer such that a(n)+p equals to a power of two, where p is the least prime larger than a(n). a(1) = 3 (3+5 = 8)
a(2) = (15+17 = 32)
a(3) = 61 (61+67 = 128)etc. 

2)
a(1) = 1 2 is a multiple of the first term, so a(2) = 2/1 = 2
Now, to get a multiple of a(2) we need to add 3 of the unused numbers (3+4+5 = 12). So, a(3) = 12/2 = 6. 
a(4) = 6/6 =1
a(5)= 7/1= 7
a(6)= (8+9+10+11+12+13)/7 = 9
a(7) = (14+15+16)/9 = 5
and so on.

3)
We have a computer program that draws 4n equal line segments in each step n. The goal is to draw as many squares (from all sizes) as possible. Ideally, we get A111715(n) squares.  However, at each step, directly after the 4n segments are drawn, another program erases n segments trying to terminate as many squares as possible. The sequence is the total number of squares in each step. 
Best,

Ali