Pell numbers: Difference between revisions

=={{header|Scala}}==

<lang scala>val pellNumbers: LazyList[BigInt] =

BigInt("0") #:: BigInt("1") #::

(pellNumbers zip pellNumbers.tail).

map{ case (a,b) => 2*b + a }

val pellLucasNumbers: LazyList[BigInt] =

BigInt("2") #:: BigInt("2") #::

(pellLucasNumbers zip pellLucasNumbers.tail).

map{ case (a,b) => 2*b + a }

val pellPrimes: LazyList[BigInt] =

pellNumbers.tail.tail.

filter{ case p => p.isProbablePrime(16) }

val pellIndexOfPrimes: LazyList[BigInt] =

pellNumbers.tail.tail.

filter{ case p => p.isProbablePrime(16) }.

map{ case p => pellNumbers.indexOf(p) }

val pellNSWnumbers: LazyList[BigInt] =

(pellNumbers.zipWithIndex.collect{ case (p,i) if i%2 == 0 => p}

zip

pellNumbers.zipWithIndex.collect{ case (p,i) if i%2 != 0 => p}).

map{ case (a,b) => a + b }

val pellSqrt2Numerator: LazyList[BigInt] =

BigInt(1) #:: BigInt(3) #::

(pellSqrt2Numerator zip pellSqrt2Numerator.tail).

map{ case (a,b) => 2*b + a }

val pellSqrt2: LazyList[BigDecimal] =

(pellSqrt2Numerator zip pellNumbers.tail).

map{ case (n,d) => BigDecimal(n)/BigDecimal(d) }

val pellSqrt2asString: LazyList[String] =

(pellSqrt2Numerator zip pellNumbers.tail).

map{ case (n,d) => s"$n/$d" }

val pellHypotenuse: LazyList[BigInt] =

pellNumbers.tail.tail.zipWithIndex.collect{ case (p,i) if i%2 != 0 => p }

val pellShortLeg: LazyList[BigInt] =

LazyList.from(3,2).map{ case s => pellNumbers.take(s).sum }

val pellTriple: LazyList[(BigInt,BigInt,BigInt)] =

(pellHypotenuse zip pellShortLeg).

map{ case (h,s) => (s,s+1,h)}

// Output

{ println("7 Tasks")

println("-------")

println(pellNumbers.take(10).mkString("1. Pell Numbers: ", ",", "\n"))

println(pellLucasNumbers.take(10).mkString("2. Pell-Lucas Numbers: ", ",", "\n"))

println((pellSqrt2asString zip pellSqrt2).take(10).

map { case (f, d) => s"$f = $d" }.

mkString("3. Square-root of 2 Approximations: \n\n",

"\n", "\n"))

println(pellPrimes.take(10).mkString("4. Pell Primes: \n\n", "\n", "\n"))

println(pellIndexOfPrimes.take(10).mkString("5. Pell Index of Primes: ", ",", "\n"))

println(pellNSWnumbers.take(10).mkString("6. Newman-Shank-Williams Numbers: \n\n", "\n", "\n"))

println(pellTriple.take(10).mkString("7. Near Right-triangle Triples: \n\n", "\n", "\n"))

}

</lang>

{{out}}

<pre style="height:48ex;overflow:scroll;>7 Tasks

-------

1. Pell Numbers: 0,1,2,5,12,29,70,169,408,985

2. Pell-Lucas Numbers: 2,2,6,14,34,82,198,478,1154,2786

3. Square-root of 2 Approximations:

1/1 = 1

3/2 = 1.5

7/5 = 1.4

17/12 = 1.416666666666666666666666666666667

41/29 = 1.413793103448275862068965517241379

99/70 = 1.414285714285714285714285714285714

239/169 = 1.414201183431952662721893491124260

577/408 = 1.414215686274509803921568627450980

1393/985 = 1.414213197969543147208121827411168

3363/2378 = 1.414213624894869638351555929352397

4. Pell Primes:

2

5

29

5741

33461

44560482149

1746860020068409

68480406462161287469

13558774610046711780701

4125636888562548868221559797461449

5. Pell Index of Primes: 2,3,5,11,13,29,41,53,59,89

6. Newman-Shank-Williams Numbers:

1

7

41

239

1393

8119

47321

275807

1607521

9369319

7. Near Right-triangle Triples:

(3,4,5)

(20,21,29)

(119,120,169)

(696,697,985)

(4059,4060,5741)

(23660,23661,33461)

(137903,137904,195025)

(803760,803761,1136689)

(4684659,4684660,6625109)

(27304196,27304197,38613965)</pre>