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A few thoughts on the subject.
Using beads to count prayers of course isn't exclusively Roman Catholic or even peculiarly Christian.
Hindus and Buddhists, who follow religions older than Christianity, use them.
As do Muslims.
And as Fr John Matusiak explains on the OCA site, the Eastern Christian practice of using a chaplet (broadly speaking, rosary) to count Jesus Prayers as part of a monastic prayer rule is older than the commonly known Dominican rosary used and loved by millions of Roman Catholics.
The Eastern Christian and Muslim practice (many Muslim practices were got from the Christian East) may be where St Dominic got the idea to use them for his rosary. (There is a legend, not RC doctrine, that he got the idea direct from the Virgin Mary in a vision.)
The Dominican rosary isn't native to the Byzantine Rite of the Eastern Orthodox tradition (it's not directly from Eastern cultures and it got started a couple of centuries after the East/West split), and since a rite is a package deal complete with its own devotional practices as well as theological expression, I reckon that most born Orthodox don't use it - with all those akathists and canons to choose from, they don't need to!
But cultures mix with trade, intermarriage etc. - there are lots of Orthodox/RC marriages in the world, for example. So it's fair to say that there are some born Orthodox who use the commonly understood rosary. A priest who lived in the Middle East told me that this cultural crossover is a fact of Christian life over there.
Did some saints like St Seraphim of Sarov have prayer rules that resembled the Dominican rosary? Yes! Things like 150 'Rejoice, O Virgin Mother of God' (the Byzantine Hail Mary) prayers - certainly a strong parallel. (Perhaps because of Russian contact with these practices from the Poles by way of the Ukrainians.)
BTW, the rosary has 150 Hail Marys because it mimics the 150 psalms read in the hours - essentially it was meant as a form of the hours for people who couldn't read, which in the Middle Ages was many people.
Repetitions of simple prayers both parallels the rosary and is native to the Byzantine Rite - not only the rule of saying the Jesus Prayer but the 12 and even 40 'Lord, have mercys' one repeats when praying the hours.
The online Eastern Orthodox world is largely a convert scene and you're not likely to find rosary-users here because not only is the practice not native to the Byzantine Rite but the converts often come from Protestant backgrounds and/or otherwise want to consciously distance themselves from the RCs.
An objection you might hear or read from the Orthodox is that the Dominican rosary uses the Western concept of 'meditating on the mysteries', 'mysteries' here not meaning 'sacraments' (as it usually does in Orthodoxspeak) but events in the lives of Mary and Jesus. The objection is that this involves fantasy or using the imagination in prayer, which can be dangerous, leading to spiritual delusion, etc.
Eastern Orthodox don't carry or use chaplets in church like RCs do rosaries - wearing the chaplet (called chotki in Slavonic/Russian) on the left wrist is only for monks and nuns. You see Orthodox bishops holding them or wearing them that way because they're monks.
The authentic tradition about layfolk having and using them is they're given to you by your spiritual father if he deems them suitable for you and you take them home and use them privately there.
I think that pretty much covers it.
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