Add ability to display specific totative digits

Instead of just saying how many totative digits there are, the new -t
flag allows the user to determine the specific digits.  All totatives
will end in one of these digits, and all primes are either factors or
totatives.  This feature is not useful in comparing radices, only
learning one you have already chosen.

Because there can be so many totatives (p - 1 of them for primes!), this
is not displayed by default.  The digit map (without -f) gives this
information, and beyond its range every number will have more than 8
totatives, so do not use this flag if you only want the count.

1 files changed, 14 insertions, 0 deletions

diff --git a/factors/totative.go b/factors/totative.go
index 680cc26..abbbe89 100644
--- a/factors/totative.go
+++ b/factors/totative.go
@@ -17,3 +17,17 @@ func Totient(n uint) uint {
 
 	return num * (n / denom)
 }
+
+// TotativeDigits returns a slice containing every number less than r
+// that is a totative of r (shares no factors with r).
+func TotativeDigits(r uint32) []uint32 {
+	digits := make([]uint32, Totient(uint(r)))
+	totativesFound := 0
+	for d := uint32(0); d < r; d++ {
+		if gcd(d, r) == 1 {
+			digits[totativesFound] = d
+			totativesFound++
+		}
+	}
+	return digits
+}