Pentagonal numbers made from pentagonal numbers Introduction
A pentagonal number (A000326) is generated by the formula Pn= 0.5×(3n2-n). Or you can just count the amount of dots used:

You can use the formula, or the gif above to find the first few pentagonal numbers:
1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176, 210, 247, 287, 330, 376, 425, 477, etc...

Next, we need to compute the sum of x consecutive numbers.
For example, if x = 4, we need to look at Pn + Pn+1 + Pn+2 + Pn+3 (which consists of 4 terms). If the sum of the pentagonal numbers also is a pentagonal number, we will call this a pentagonal pentagon number.
For x = 4, the smallest pentagonal pentagon number is 330, which is made of 4 consecutive pentagonal numbers: 51, 70, 92, 117. So, when the input is 4, your program of function should output 330.

Task

When given an integer greater than 1, output the smallest pentagonal pentagon number.
You may provide a function or a program.
Note: There are no solutions for e.g. x = 3. This means that if a number cannot be made from the first 10000 pentagonal numbers, you must stop computing and output whatever fits best for you.
This is code-golf, so the submission with the least amount of bytes wins!


Test cases:
Input: 2
Output: 1926 (which comes from 925, 1001)

Input: 3
Output: ?

Input: 4
Output: 330 (which comes from 51, 70, 92, 117)

Input: 5
Output: 44290 (which comes from 8400, 8626, 8855, 9087, 9322)

Input: 6
Output: 651 (which comes from 51, 70, 92, 117, 145, 176)

Input: 7
Output: 287 (which comes from 5, 12, 22, 35, 51, 70, 92)

Input: 8
Output: ?

Input: 9
Output: 12105 (which comes from 1001, 1080, 1162, 1247, 1335, 1426, 1520, 1617, 1717)

Input: 10
Output: ?

Also bigger numbers can be given:
Input: 37
Output: 32782

Input: 55
Output: 71349465

Input: 71
Output: 24565290
CJam, 29 bytes

6e5{)_3*(*2/}%_A4#&lt;riew::+&amp;1&lt;


Try it online.

Takes a couple of seconds to run.

Explanation

First, we need to check how many pentagonal numbers we need to consider as potential sums. The sum of the first 10,000 pentagonal numbers is 500050000000. The first pentagonal number greater than that is the 577,380th.

6e5       e# 600,000 (a short number that's a bit bigger than we need).
{         e# Map this block onto every number from 0 to 599,999...
  )       e#   Increment.
  _3*(*2/ e#   Apply the pentagonal number formula given in the challenge.
}%
_         e# Make a copy.
A4#&lt;      e# Truncate to the first 10,000 elements.
ri        e# Read input and convert to integer.
ew        e# Get sublists of that length.
::+       e# Sum each sublist.
&amp;         e# Set intersection with all 600k pentagonal numbers computed earlier.
1&lt;        e# Truncate to the first result.


I used a slightly modified program to find the largest inputs which yield a non-empty solution. These are all the solutions for inputs greater than 9,000:

9919 -&gt; 496458299155
9577 -&gt; 446991927537
9499 -&gt; 455533474060
9241 -&gt; 401702906276
9017 -&gt; 429351677617