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A020342.java
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package irvine.oeis.a020;
import irvine.factor.factor.Jaguar;
import irvine.math.IntegerUtils;
import irvine.math.z.Z;
import irvine.oeis.Sequence1;
/**
* A020342 Vampire numbers: (definition 1): n has a nontrivial factorization using n's digits.
* @author Sean A. Irvine
*/
public class A020342 extends Sequence1 {
private Z mN = Z.valueOf(125);
private boolean isOk(final int[] s, Z v) {
boolean ok = true;
while (!v.isZero()) {
if (--s[(int) v.mod(10)] < 0) {
ok = false;
}
v = v.divide(10);
}
return ok;
}
private void replace(final int[] s, Z v) {
while (!v.isZero()) {
++s[(int) v.mod(10)];
v = v.divide(10);
}
}
private boolean isVampire(final Z n, final Z[] div, final int pos, final int[] syndrome) {
if (Z.ONE.equals(n)) {
return IntegerUtils.isZero(syndrome);
}
for (int k = pos; k < div.length; ++k) {
final Z[] qr = n.divideAndRemainder(div[k]);
if (qr[1].isZero()) {
if (isOk(syndrome, div[k]) && isVampire(qr[0], div, k, syndrome)) {
return true;
}
replace(syndrome, div[k]);
}
}
return false;
}
private int[] syndrome(final Z n) {
final int[] s = new int[10];
replace(s, n);
return s;
}
@Override
public Z next() {
while (true) {
mN = mN.add(1);
final int[] syndrome = syndrome(mN);
final Z[] d = Jaguar.factor(mN).divisors();
final Z[] proper = new Z[d.length - 2];
for (int k = 0, j = 0; k < d.length; ++k) {
if (!mN.equals(d[k]) && !Z.ONE.equals(d[k])) {
proper[j++] = d[k];
}
}
if (isVampire(mN, proper, 0, syndrome)) {
return mN;
}
}
}
}