Zsh, 50 30 2934 bytes
Bug fix: I was checking each pair of letters to make sure it had a character of each parity, instead of ensuring it alternated.
"e"cho E" "{"1"'.'.999"9"'.'.2''0'2} E [Try it online!][TIO-k4dhoo94] Try it online! Try it online!Try it online! Zsh: https://www.zsh.org/ [TIO-k4dhoo94]: https://tio.run/##RU5LCsIwFFybUwyvkSbUjRURaysKtiAIXkCEfiJd@cS46ufsMV2Iuxnm29nW1eUHe9h3jTRFmF@L0JVVppZYYY0NttCCDNUtI7/NZH8vq/GPftz5nBCdbaciIR78hgFDkezVwSaJJqlSL2kaSe/QsFDqxTbK4gVUYBAhYI05Yq0xDDDTHBXH8yU/wf@T3ptAGskkGn4a9wU "Zsh – Try It Online"
Self-tests. Contains a literal tab.
I couldn't figure out a way to finagle the most straightforward EDIT: I did it. Turns out in normal expressions, quotes inside brace ranges don't really matter.echo E\ {1..99..2} E into anything, mostly due to the double period.