I don't know what is normal. I don't think there is a norm, just individual preferences or tendencies.
I can go two weeks without contacting someone I am interested in. The time just flies I by. I feel really bad about it though. It's not even that I don't think about them (I may think about them
a lot), but I am afraid to act in reality sometimes. It feels so much safer to never talk to people...
When I
really, really, really like someone romantically, more than a few days of not hearing from them can feel like an eternity, and yet I still will wait for them to initiate contact. Because it's so easy for me to lose track of time, I give other people the benefit of the doubt and wait a week or so and then if I cannot stand it I contact them. Ideally, I would talk to them briefly once a day, or a few texts and emails. More than that might make me feel smothered. However, the more I like someone, the less it feels they are intruding on my time, and I will make it a priority to respond and keep in contact.
If I am not really into someone, then hearing from them more than a few times a week can annoy me. I feel like they are interrupting my space and not giving me a chance to come to them when I am ready. At some point I will come to them, but it's often too late on their timetable. I've realized that when I am this way, it's my way of telling myself, "You're just not that into him".
This is all bad, bad, bad though....probably why I am always single and just ran off over 5 guys in three months
Ultimately, for me & the guys I date, it's in both of our best interests if they pursue without too much letup (maybe starting off a little slowly though).