Jacobsthal numbers: Difference between revisions

import java.math.BigInteger;

public final class JacobsthalNumbers {

public static void main(String[] aArgs) {

System.out.println("The first 30 Jacobsthal Numbers:");

for ( int i = 0; i < 6; i++ ) {

for ( int k = 0; k < 5; k++ ) {

System.out.print(String.format("%15s", jacobsthalNumber(i * 5 + k)));

}

System.out.println();

}

System.out.println();

System.out.println("The first 30 Jacobsthal-Lucas Numbers:");

for ( int i = 0; i < 6; i++ ) {

for ( int k = 0; k < 5; k++ ) {

System.out.print(String.format("%15s", jacobsthalLucasNumber(i * 5 + k)));

}

System.out.println();

}

System.out.println();

System.out.println("The first 20 Jacobsthal oblong Numbers:");

for ( int i = 0; i < 4; i++ ) {

for ( int k = 0; k < 5; k++ ) {

System.out.print(String.format("%15s", jacobsthalOblongNumber(i * 5 + k)));

}

System.out.println();

}

System.out.println();

System.out.println("The first 10 Jacobsthal Primes:");

for ( int i = 0; i < 10; i++ ) {

System.out.println(jacobsthalPrimeNumber(i));

}

}

private static BigInteger jacobsthalNumber(int aIndex) {

BigInteger value = BigInteger.valueOf(parityValue(aIndex));

return BigInteger.ONE.shiftLeft(aIndex).subtract(value).divide(THREE);

}

private static long jacobsthalLucasNumber(int aIndex) {

return ( 1 << aIndex ) + parityValue(aIndex);

}

private static long jacobsthalOblongNumber(int aIndex) {

long nextJacobsthal = jacobsthalNumber(aIndex + 1).longValueExact();

long result = currentJacobsthal * nextJacobsthal;

currentJacobsthal = nextJacobsthal;

return result;

}

private static long jacobsthalPrimeNumber(int aIndex) {

BigInteger candidate = jacobsthalNumber(latestIndex++);

while ( ! candidate.isProbablePrime(CERTAINTY) ) {

candidate = jacobsthalNumber(latestIndex++);

}

return candidate.longValueExact();

}

private static int parityValue(int aIndex) {

return ( aIndex & 1 ) == 0 ? +1 : -1;

}

private static long currentJacobsthal = 0;

private static int latestIndex = 0;

private static final BigInteger THREE = BigInteger.valueOf(3);

private static final int CERTAINTY = 20;

}

The 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

The 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

The 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

The first 10 Jacobsthal Primes:

3

5

11

43

683

2731

43691

174763

2796203

715827883