I was hoping to harvest beet seeds; I let one 'go to seed' this year, but it stayed green, never seeming to 'mature'. Oh, well, maybe it was just our weather this year. I will probably try again next year.
Beets are a biennial and so will not flower and go to seed in its first year. Being you are in Alaska, it is too cold for beets to over winter there. It is a pain to get seeds for your climate. The plants need to cut back, dug and stored with the roots in damp sand in a cool location all winter and then replanted in the spring.