Jacobsthal numbers
Jacobsthal numbers are an integer sequence related to Fibonacci numbers. Similar to Fibonacci, where each term is the sum of the previous two terms, each term is the sum of the previous, plus twice the one before that. Traditionally the sequence starts with the given terms 0, 1.
J0 = 0
J1 = 1
Jn = Jn-1 + 2 × Jn-1
Terms may be directly calculated using the formula:
J(n) = ( 2n - (-1)n ) / 3
Jacobsthal oblong numbers is the sequence obtained from multiplying each two consecutive Jacobsthal numbers together.
Jacobsthal primes are Jacobsthal numbers that are prime.
- Task
- Find and display the first 30 Jacobsthal numbers
- Find and display the first 20 Jacobsthal oblong numbers
- Find and display at least the first 10 Jacobsthal primes
- See also
Raku
<lang perl6>my $jacobsthal = cache lazy (^∞).hyper.map: { (exp($_, 2) - exp($_, -1)) / 3 };
say "First 30 Jacobsthal numbers:"; say $jacobsthal[^30].batch(5)».fmt("%9d").join: "\n";
say "\n\nFirst 20 Jacobsthal oblong numbers:"; say (^∞).map( { $jacobsthal[$_] × $jacobsthal[$_+1] } )[^20].batch(5)».fmt("%11d").join: "\n";
say "\n\nFirst 20 Jacobsthal primes:"; say $jacobsthal.grep( &is-prime )[^20].join: "\n";</lang>
- 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 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