I have what was called a pencil cactus. I haven't found out which one it is. Anyone know?

Usually what is referred to as 'Pencil Cactus' is Euphorbia tirucalli. Not a cactus.
I haven't seen your cactus before but it is very pretty!

All I've ever seen is the Euphorbia Tirucalli, but there's also some called Pencil Cholla. There aren't a lot of pictures, but take a look -
http://garden.org/plants/searc...

I agree about the Euphorbia tirucalli being called that also. This one is super easy to grow. A few pieces fell off and they rooted and started growing quickly. I have it outdoors in 7b and it's totally happy. I found something similar called Cylindropuntia kleiniae.

There are some serious spines on those, but they are beautiful.

with Ibis, it looks a lot like Diamond Cholla (Cylindropuntia ramosissima)

It does look like that Deb, but the spines on mine aren't quite as heavy or long. I guess it could be due to growing conditions being different. A lot of the cacti and succulent vary due to different conditions and care.

Let's see if @Baja_Costero has any ideas.

Looks like a cholla, Cylindropuntia, but I don't know which one.

I wrote High Country Gardens and they said they'd be happy to ID it, so I just sent them the pics. I'll let you know when I hear.

Deebie is pretty much correct, it is cylindropuntia ramosissima var. nudum (as in [mostly] spineless) and AFAIK it is called the 'Diamond Cholla', following the pattern on the stems. Indeed the name 'Pencil Cholla' is usually reserved for C. kleiniae.

I have this growing in my yard and the plant came from the Phoenix Desert Botanical Garden. It occurs in the wild in southern Arizona and presumably across the border in Mexico. Is extremely drought tolerant and has really pretty flowers as apparent from the picture in the OP. The spined version is does really cool things with the light if it catches low angle sun... when I get home I will try and find the picture and post it to demonstrate that...

I'd love to see a pic of the one you have in your yard!

OK my post just went missing so if there end up being two with the same pictures, sorry!

The first pic is of the plant I have, the pic is about 3 years old since then I have only flower pics, the plant has grown some. The second pic is of the spiny variety that with the right light angle looks really really good.

Your first pic is just like mine, and I see what you mean about the one in the second pic. Very nice!