I want to perform a card trick using a normal pack of 52 cards as follows:

Hold the pack with the cards facing down.
Take the top card and move it to the bottom of the deck and say out loud “A”.
Take the top card and move it to the bottom of the deck and say out loud “C”.
Take the top card and move it to the bottom of the deck and say out loud “E”.
Turn over the top card and place it face up on the table and say “SPELLS ACE”.
The card should be the Ace of Clubs.

Take the top card and move it to the bottom of the deck and say out loud “T”.
Take the top card and move it to the bottom of the deck and say out loud “W”.
Take the top card and move it to the bottom of the deck and say out loud “O”.
Turn over the top card and place it face up on top of the Ace of Clubs and say “SPELLS TWO”.
The card should be the Two of Clubs.

Continue to spell out THREE……JACK QUEEN KING and turn over the matching card in Clubs.
Then Ace to King of Diamonds, then Hearts, then Spades.

What is the sequence of the cards I require in my deck to perform the trick?
Give 2 non-computerised methods of solving the problem.