Puzzle #122: Which page does Dithering Dan land on?

#122 Article of faith

Dithering Dan has just received his monthly copy of Doubtful Daze magazine. Unsure which article to read first, he turns to a random page and counts a certain number of pages forwards, increasing the page number. He then counts half of his previous page count back, then half the previous count forwards, and finally half the last count back. The page number he finishes on turns out to be four times the one he started at. There are fewer than 50 pages in the magazine and the pages are numbered consecutively starting at page 1.

What…