Stream<Pair> pairStream = Streams.iterate(0, (i) -> i + 1).map( // natural numbers
    new Function<Integer, Pair>() {
        Integer previous;

        @Override
        public Pair apply(Integer integer) {
            Pair pair = null;
            if (previous != null) pair = new Pair(previous, integer);
            previous = integer;
            return pair;
        }
    }).substream(1); // drop first null

pairStream.limit(1_000_000).forEach(i -> System.out.println(i));

IntStream.range(1, arrayList.size())
             .mapToObj(i -> new Pair(arrayList.get(i-1), arrayList.get(i)))
             .forEach(System.out::println);

public class ConsecutiveSpliterator<T> implements Spliterator<List<T>> {

    private final Spliterator<T> wrappedSpliterator;

    private final int n;

    private final Deque<T> deque;

    private final Consumer<T> dequeConsumer;

    public ConsecutiveSpliterator(Spliterator<T> wrappedSpliterator, int n) {
        this.wrappedSpliterator = wrappedSpliterator;
        this.n = n;
        this.deque = new LinkedList<>();
        this.dequeConsumer = new Consumer<T>() {
            @Override
            public void accept(T t) {
                deque.addLast(t);
            }
        };
    }

    @Override
    public boolean tryAdvance(Consumer<? super List<T>> action) {
        deque.pollFirst();
        fillDeque();
        if (deque.size() == n) {
            List<T> list = new ArrayList<>(deque);
            action.accept(list);
            return true;
        } else {
            return false;
        }
    }

    private void fillDeque() {
        while (deque.size() < n && wrappedSpliterator.tryAdvance(dequeConsumer))
            ;
    }

    @Override
    public Spliterator<List<T>> trySplit() {
        return null;
    }

    @Override
    public long estimateSize() {
        return wrappedSpliterator.estimateSize();
    }

    @Override
    public int characteristics() {
        return wrappedSpliterator.characteristics();
    }
}

public <E> Stream<List<E>> consecutiveStream(Stream<E> stream, int n) {
    Spliterator<E> spliterator = stream.spliterator();
    Spliterator<List<E>> wrapper = new ConsecutiveSpliterator<>(spliterator, n);
    return StreamSupport.stream(wrapper, false);
}

consecutiveStream(Stream.of(0, 1, 2, 3, 4, 5), 2).map(
    new Function<List<Integer>, Pair>() {
        public Pair apply(List<Integer> list) {
            return new Pair(list.get(0), list.get(1));
        }
    }).forEach(System.out::println);

import java.util.function.IntFunction;
import java.util.stream.IntStream;

public class PairFunction implements IntFunction<PairFunction.Pair> {

  public static class Pair {

    private final int first;
    private final int second;

    public Pair(int first, int second) {
      this.first = first;
      this.second = second;
    }

    @Override
    public String toString() {
      return "[" + first + "|" + second + "]";
    }
  }

  private int last;
  private boolean first = true;

  @Override
  public Pair apply(int value) {
    Pair pair = !first ? new Pair(last, value) : null;
    last = value;
    first = false;
    return pair;
  }

  public static void main(String[] args) {

    IntStream intStream = IntStream.of(0, 1, 2, 3, 4);
    final PairFunction pairFunction = new PairFunction();
    intStream.mapToObj(pairFunction)
        .filter(p -> p != null) // filter out the null
        .forEach(System.out::println); // display each Pair

  }

}

List<Integer> input = Arrays.asList(0, 1, 2, 3, 4);
Stream<Pair> pairStream = Streams.zip(input.stream(),
                                      input.stream().substream(1),
                                      (a, b) -> new Pair(a, b)
);

public static void main(String[] args) {
    Stream<Integer> numbers = IntStream.rangeClosed(0, 4).boxed();
    AtomicInteger counter = new AtomicInteger(Integer.MIN_VALUE);
    List<Pair> collect = numbers.map(n -> {
                            int i = counter.getAndSet(n);
                            return i == Integer.MIN_VALUE ? null : new Pair(i, n);
                        })
                        .filter(p -> p != null)
                        .collect(toList());
    System.out.println(collect);
}

class Pair {
    private int left, right;
    Pair(int left, int right) { this.left = left; this.right = right; }
    @Override public String toString() { return "{" + left + "," + right + '}'; }
}

for(int i = 0 ; i < stream.length-1 ; i++)
{
    Pair pair = new Pair(stream[i], stream[i+1]);
    // then add your pair to an array
}