Here is another solution, using apply() and lapply().

# list of sequences corresponding to each row in data1:
seqlist <- apply(data1, 1, function(x)seq(from=x[1], to=x[2]))

# Find which rows of data2 are inside those sequences:
rowsInSeq<- unlist(lapply(seqlist , function(x)which(data2$position %in%
x)))

# use that to index data1:
data2[rowsInSeq,]


greetings,
remko

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