Pell numbers: Difference between revisions

=={{header|Java}}==

<syntaxhighlight lang="java">

import java.math.BigDecimal;

import java.math.BigInteger;

import java.math.MathContext;

import java.util.ArrayList;

import java.util.List;

public final class PellNumbers {

public static void main(String[] aArgs) {

System.out.println("7 Tasks");

System.out.println("-------");

System.out.println("Task 1, Pell Numbers: " + pellNumbers(TERM_COUNT));

System.out.println();

System.out.println("Task 2, Pell-Lucas Numbers: " + pellLucasNumbers(TERM_COUNT));

System.out.println();

System.out.println("Task 3, Approximations to square root of 2:");

List<Rational> rationals = squareRoot2(TERM_COUNT + 1);

for ( int i = 1; i < TERM_COUNT + 1; i++ ) {

System.out.println(rationals.get(i) + " = " + rationals.get(i).toBigDecimal());

}

System.out.println();

List<Pair> pairs = pellPrimes(TERM_COUNT);

System.out.println("Task 4, Pell primes:");

for ( int i = 0; i < TERM_COUNT; i++ ) {

System.out.println(pairs.get(i).pellPrime);

}

System.out.println();

System.out.print("Task 5, Pell indices of Pell primes:");

for ( int i = 0; i < TERM_COUNT; i++ ) {

System.out.print(pairs.get(i).index + " ");

}

System.out.println();

System.out.println();

System.out.println("Task 6, Newman-Shank-Williams numbers: " + newmanShankWilliams(TERM_COUNT));

System.out.println();

System.out.println("Task , Near isoseles right triangles:");

List<Triple> nearIsoselesRightTriangles = nearIsoslesRightTriangles(TERM_COUNT);

for ( int i = 0; i < TERM_COUNT; i++ ) {

System.out.println(nearIsoselesRightTriangles.get(i));

}

}

private static List<BigInteger> pellNumbers(int aTermCount) {

PellIterator pellIterator = new PellIterator(BigInteger.ZERO, BigInteger.ONE);

List<BigInteger> result = new ArrayList<BigInteger>();

for ( int i = 0; i < aTermCount; i++ ) {

result.add(pellIterator.next());

}

return result;

}

private static List<BigInteger> pellLucasNumbers(int aTermCount) {

PellIterator pellLucasIterator = new PellIterator(BigInteger.TWO, BigInteger.TWO);

List<BigInteger> result = new ArrayList<BigInteger>();

for ( int i = 0; i < aTermCount; i++ ) {

result.add(pellLucasIterator.next());

}

return result;

}

private static List<Rational> squareRoot2(int aTermCount) {

PellIterator pellIterator = new PellIterator(BigInteger.ZERO, BigInteger.ONE);

PellIterator pellLucasIterator = new PellIterator(BigInteger.TWO, BigInteger.TWO);

List<Rational> result = new ArrayList<Rational>();

for ( int i = 0; i < aTermCount; i++ ) {

result.add( new Rational(pellLucasIterator.next().divide(BigInteger.TWO), pellIterator.next()) );

}

return result;

}

private static List<Pair> pellPrimes(int aTermCount) {

PellIterator pellIterator = new PellIterator(BigInteger.ZERO, BigInteger.ONE);

int index = 0;

int count = 0;

List<Pair> result = new ArrayList<Pair>();

while ( count < aTermCount ) {

BigInteger pellNumber = pellIterator.next();

if ( pellNumber.isProbablePrime(16) ) {

result.add( new Pair(pellNumber, index) );

count += 1;

}

index += 1;

}

return result;

}

private static List<BigInteger> newmanShankWilliams(int aTermCount) {

PellIterator pellIterator = new PellIterator(BigInteger.ZERO, BigInteger.ONE);

List<BigInteger> result = new ArrayList<BigInteger>();

for ( int i = 0; i < aTermCount; i++ ) {

BigInteger pellNumber = pellIterator.next();

result.add(pellNumber.add(pellIterator.next()));

}

return result;

}

private static List<Triple> nearIsoslesRightTriangles(int aTermCount) {

PellIterator pellIterator = new PellIterator(BigInteger.ZERO, BigInteger.ONE);

pellIterator.next();

List<Triple> result = new ArrayList<Triple>();

BigInteger sum = pellIterator.next();

for ( int i = 0; i < aTermCount; i++ ) {

sum = sum.add(pellIterator.next());

BigInteger nextTerm = pellIterator.next();

result.add( new Triple(sum, sum.add(BigInteger.ONE), nextTerm) );

sum = sum.add(nextTerm);

}

return result;

}

private static class PellIterator {

public PellIterator(BigInteger aFirst, BigInteger aSecond) {

a = aFirst; b = aSecond;

}

public BigInteger next() {

aCopy = a;

bCopy = b;

b = b.add(b).add(a);

a = bCopy;

return aCopy;

}

private BigInteger a, aCopy, b, bCopy;

}

private static record Rational(BigInteger numerator, BigInteger denominator) {

public BigDecimal toBigDecimal() {

return new BigDecimal(numerator).divide( new BigDecimal(denominator), mathContext );

}

public String toString() {

return numerator + " / " + denominator;

}

private static MathContext mathContext = new MathContext(34);

}

private static record Pair(BigInteger pellPrime, int index) {}

private static record Triple(BigInteger shortSide, BigInteger longSide, BigInteger hypotenuse) {

public String toString() {

return "(" + shortSide + ", " + longSide + ", " + hypotenuse + ")" ;

}

}

private static final int TERM_COUNT = 10;

}

</syntaxhighlight>

{{ out }}

<pre>

7 Tasks

-------

Task 1, Pell Numbers: [0, 1, 2, 5, 12, 29, 70, 169, 408, 985]

Task 2, Pell-Lucas Numbers: [2, 2, 6, 14, 34, 82, 198, 478, 1154, 2786]

Task 3, Approximations to square root of 2:

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

Task 4, Pell primes:

2

5

29

5741

33461

44560482149

1746860020068409

68480406462161287469

13558774610046711780701

4125636888562548868221559797461449

Task 5, Pell indices of Pell primes:2 3 5 11 13 29 41 53 59 89

Task 6, Newman-Shank-Williams numbers: [1, 7, 41, 239, 1393, 8119, 47321, 275807, 1607521, 9369319]

Task , Near isoseles right triangles:

(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>