I'm pretty sure the Doctor does think about his former companions from time to time, even if he rarely mentions them. Most of them, anyway. There are those (such as Adric) who have painful memories associated with them, so he probably avoids thinking about them as much as possible. Indeed, that scene in "The Power Of Three" where the Doctor tells Brian what happened to his former companions, including the fact that a few of them died, is the closest he has come to mentioning Adric since the series was revived. Not that Adric is likely to receive a more direct mention, unless the Doctor were to meet Romana again and had to break the news of the boy's fate. However, for that to happen, there would be the "small matter" of getting Romana out of E-Space or the Doctor back into E-Space - and, according to "Earthshock", that was difficult even before the Time War.
As for Captain Jack, who knows? The last time we saw him in the main series was at that space-bar towards the end of "The End Of Time: Part Two".
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