Generate Some Secure PINs Inspired by this badly received migrated post.

The head of security at your company is concerned about your PIN generating system after it gave him 12345. He also didn't really appreciate the Spaceballs joke you made at his expense, so you've been delegated to re-write the PIN generator. Since it has to fit on some special hardware, you have to make it as small as possible.

Your Task


You take two inputs - # of PINs, and PIN size in digits.
Generate the specified number of PINs of the specified size randomly and print it out.
All valid PIN's of the size must be possible to be printed out, even if they aren't uniformly probable.
However, there are some restrictions on the PINs - here are the invalid ones:


If all the pairs are the same digit: 114422 (Note: this will obviously include all same digit PINs).
Increasingly linear PINs (mod 10): 246802.
All groups of 3 are physical lines on the keypad of 1 2 3;4 5 6;7 8 9;bksp 0 enter;: 147369.
The PIN can be entirely split up into groups from rule 1 and rule 3.






This is code-golf, so shortest code in bytes wins!
Pyth, 120 bytes

Arz7VGJ1WJK%"%0*d",HO-^TH1=J|q1l{m%-F_vMcd1T.:K2u|GHmu|GHm?qlk2:k"(.)\\1"0?qlk3}k+++=bcS"123456789"3_Mb.Tb_M.TbZdZ./K0)K


Figured I should add a real implementation then. Generates random numbers until one is found that meets all requirements. Can probably be improved a lot!

Online version