x <- logical(100)
y <- lapply(1:length(x), function(i) sapply(1:length(x), function(j) if (j%%i==0) !x[j] else x[j]))
which(sapply(1:length(x), function(j) sum(sapply(sapply(1:length(y), function(i) y[i]), `[`, j))) %% 2 == 1)
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