"Double" and "Triple" HP Washing?

"Double" Wash: Miserably described it correctly.
"Triple" Wash: iFrancisco described it correctly.

As for MP Gain, there are two different cases.
(All stuff below is for thief/archer.)
Level-Up
HP Gain: +20~24
MP Gain: +14~16 + Floor(INT/10)

Adding AP
Add AP to HP: +16~20
Add AP to MP: +10~12 + Floor(INT*.075)
NOTE: Since people are quoting this formula I posted a while back... I'm not absolutely certain about this formula for MP Gain, but I have yet to see a case disproving it.

And for gain/loss when using AP Resets:
AP Reset
Add to HP: +16
MP Loss: -12

If you want to guarantee "double"/"triple" wash each level from just the "Adding AP" part:
You need 187/347 INT.

If you want to factor in the MP gain from the levelup part:
You need 150/approx. 280 INT.