I've found this sequence similar to Marcin Ciura's sequence:

```
1, 4, 9, 23, 57, 138, 326, 749, 1695, 3785, 8359, 18298, 39744, etc.
```

For example, Ciura's sequence is:

```
1, 4, 10, 23, 57, 132, 301, 701, 1750
```

This is a mean of prime numbers. Python code to find mean of prime numbers is here:

```
import numpy as np
def isprime(n):
''' Check if integer n is a prime '''
n = abs(int(n)) # n is a positive integer
if n < 2: # 0 and 1 are not primes
return False
if n == 2: # 2 is the only even prime number
return True
if not n & 1: # all other even numbers are not primes
return False
# Range starts with 3 and only needs to go up the square root
# of n for all odd numbers
for x in range(3, int(n**0.5)+1, 2):
if n % x == 0:
return False
return True
# To apply a function to a numpy array, one have to vectorize the function
vectorized_isprime = np.vectorize(isprime)
a = np.arange(10000000)
primes = a[vectorized_isprime(a)]
#print(primes)
for i in range(2,20):
print(primes[0:2**i].mean())
```

The output is:

```
4.25
9.625
23.8125
57.84375
138.953125
326.1015625
749.04296875
1695.60742188
3785.09082031
8359.52587891
18298.4733887
39744.887085
85764.6216431
184011.130096
392925.738174
835387.635033
1769455.40302
3735498.24225
```

The gap in the sequence is slowly decreasing from 2.5 to 2.
Maybe this association could improve the Shellsort in the future.