Jacobsthal numbers

my $jacobsthal = cache lazy 0, 1, * × 2 + * … *;
my $jacobsthal-lucas = lazy 2, 1, * × 2 + * … *;

say "First 30 Jacobsthal numbers:";
say $jacobsthal[^30].batch(5)».fmt("%9d").join: "\n";

say "\nFirst 30 Jacobsthal-Lucas numbers:";
say $jacobsthal-lucas[^30].batch(5)».fmt("%9d").join: "\n";

say "\nFirst 20 Jacobsthal oblong numbers:";
say (^∞).map( { $jacobsthal[$_] × $jacobsthal[$_+1] } )[^20].batch(5)».fmt("%11d").join: "\n";

say "\nFirst 20 Jacobsthal primes:";
say $jacobsthal.grep( &is-prime )[^20].join: "\n";

Output:

First 30 Jacobsthal numbers:
        0         1         1         3         5
       11        21        43        85       171
      341       683      1365      2731      5461
    10923     21845     43691     87381    174763
   349525    699051   1398101   2796203   5592405
 11184811  22369621  44739243  89478485 178956971

First 30 Jacobsthal-Lucas numbers:
        2         1         5         7        17
       31        65       127       257       511
     1025      2047      4097      8191     16385
    32767     65537    131071    262145    524287
  1048577   2097151   4194305   8388607  16777217
 33554431  67108865 134217727 268435457 536870911

First 20 Jacobsthal oblong numbers:
          0           1           3          15          55
        231         903        3655       14535       58311
     232903      932295     3727815    14913991    59650503
  238612935   954429895  3817763271 15270965703 61084037575

First 20 Jacobsthal primes:
3
5
11
43
683
2731
43691
174763
2796203
715827883
2932031007403
768614336404564651
201487636602438195784363
845100400152152934331135470251
56713727820156410577229101238628035243
62357403192785191176690552862561408838653121833643
1046183622564446793972631570534611069350392574077339085483
267823007376498379256993682056860433753700498963798805883563
5562466239377370006237035693149875298444543026970449921737087520370363869220418099018130434731
95562442332919646317117537304253622533190207882011713489066201641121786503686867002917439712921903606443