ch-168; Perrin Prime and Home Prime

2 files changed, 81 insertions, 0 deletions

diff --git a/challenge-168/rick-bychowski/raku/ch-1.raku b/challenge-168/rick-bychowski/raku/ch-1.raku
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+#!/usr/bin/env raku
+
+#`{
+Task 1: Perrin Prime - Calculate the first 13 Perrin Primes.
+
+The Perrin sequence is defined to start with [3, 0, 2];
+    after that, term N is the sum of terms N-2 and N-3.
+    (So it continues 3, 2, 5, 5, 7, ….)
+A Perrin prime is a number in the Perrin sequence which is also a prime number.
+
+EXAMPLE
+f(13) = [2, 3, 5, 7, 17, 29, 277, 367, 853, 14197, 43721, 1442968193, 792606555396977]
+}
+
+sub MAIN(Int $n) {
+    say "f($n) = ", pp($n);
+}
+
+sub pp(Int $n) {
+    my @seed = <3 0 2>;
+    my %pp;
+    for 1 .. * -> $i {
+        my $ppn = @seed[*-3] + @seed[*-2];
+        @seed.push($ppn);
+        %pp{$ppn} = 1 if $ppn.is-prime;
+        last if %pp.elems == $n;
+    }
+    my @pp = %pp.keys.map({.Int}).sort;
+}
+
diff --git a/challenge-168/rick-bychowski/raku/ch-2.raku b/challenge-168/rick-bychowski/raku/ch-2.raku
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+#!/usr/bin/env raku
+
+#`{
+Task 2: HOME PRIME
+You are given an integer greater than 1.
+Write a script to find the home prime of the given number.
+
+In number theory, the home prime HP(n) of an integer n greater than 1 is the
+    prime number obtained by repeatedly factoring the increasing concatenation
+    of prime factors including repetitions.
+
+REFERENCE
+https://en.wikipedia.org/wiki/Home_prime
+https://oeis.org/A037274
+
+EXAMPLE
+HP(10) = 773,  as
+    10 factors as 2×5 yielding HP10(1) = 25,
+    25 factors as 5×5 yielding HP10(2) = HP25(1) = 55,
+    55 = 5×11 implies HP10(3) = HP25(2) = HP55(1) = 511,
+    511 = 7×73 gives HP10(4) = HP25(3) = HP55(2) = HP511(1) = 773, a prime number.
+
+}
+
+sub MAIN(Int $n where $n > 1) {
+    say factor($n);
+}
+
+sub factor(Int $n, $hpn = '') {
+    my Int $f1;
+    my Int $f2;
+    my $hp = $hpn;
+    for 2 ..^ $n -> $i {
+        if $n %% $i {
+            $f1 = $i;
+            $f2 = Int($n/$i);
+            last;
+        }
+    }
+    if $f1.defined {
+        $hp ~= $f1;
+        if $f2.is-prime {
+            $hp ~= $f2;
+            factor(Int($hp));
+        } else {
+            factor($f2, $hp);
+        }
+    } else {
+        return $n;
+    }
+}