No. There is no actual way to say this, and no way to confirm if even if it were true, unless Nintendo came out and said it
While you have noticed a half pattern it doesn't really follow right. Okay so it was;
Pokémon Red/Green/Blue - Game Boy
Pokémon Yellow - Gameboy Color
Pokémon Gold/Silver - Gameboy Color
Pokémon Crystal - Gameboy Color
Pokémon Ruby and sapphire - Gameboy Advance
Pokémon FireRed/LeafGreen - Gameboy Advance
Pokémon Emerald- Gameboy Advance
Pokémon Diamond/Pearl - Nintendo DS
Pokémon Platinum - Nintendo DS
Pokémon Heartgold/Soulsilver - Nintendo DS
Pokémon Black/White - Nintendo DS
Pokémon Black2/White2 - Nintendo 3DS/Nintendo DS
Pokémon X/Y - Nintendo 3DS
but every time a Pokémon game came out on a new handheld, the next game would be a remake.
Technically no. The Gameboy Color had no remake (Excuseable since they only did the Second and First gens by that time). Additionally, Pokémon B2W2 was technically released on 3DS, as well as DS. That makes X/Y the Second game on the 3DS. And it's not a remake. Also on the GBA and DS there were 2 remakes - one of a previous generation, one of that generation (DP --> Platinum, RS ---> Emerald). Additionally, everyone was 'predicting' with Black/White Nintendo would follow their previous pattern and release a Third game, Something like Pokémon Grey. Guess what. They didn't.
Personally I think your pattern is a little off, and even if it was right it would be impossible to confirm anything. And the fact Nintendo has no logic, so their patterns shouldn't either.