Computation of Ulam Primes in C++ Translation from Python by James Pate Williams, Jr (c) 2008 – 2023.

/*
	Translator: James Pate Williams, Jr. (c) 2008

	Translated to C++ from the following python code:

	http://en.wikipedia.org/wiki/Ulam_numbers
	https://oeis.org/A002858

	ulam_i = [1,2,3]
	ulam_j = [1,2,3]
	for cand in range(4,5000):
		res = []
		for i in ulam_i:
			for j in ulam_j:
				if i == j or j > i: pass
				else:
					res.append(i+j)
				if res.count(cand) == 1:
				ulam_i.append(cand)
				ulam_j.append(cand)
			print ulam_i

	Find the Ulam primes <= 5000
*/

#include "stdafx.h"
#include <time.h>
#include <iomanip>
#include <iostream>
#include <vector>
using namespace std;

bool sieve[10000000];

void PopulateSieve(bool *sieve, int number) {

	// sieve of Eratosthenes

	int c, inc, i, n = number - 1;

	for (i = 0; i < n; i++)
		sieve[i] = false;

	sieve[1] = false;
	sieve[2] = true;

	for (i = 3; i <= n; i++)
		sieve[i] = (i & 1) == 1 ? true : false;

	c = 3;

	do {
		i = c * c;
		inc = c + c;

		while (i <= n) {
			sieve[i] = false;
			i += inc;
		}

		c += 2;
		while (!sieve[c])
			c++;
	} while (c * c <= n);
}

bool CountEqualOne(int number, vector<int> ulam) {
	int count = 0, i;

	for (i = 0; i < ulam.size(); i++)
		if (ulam[i] == number)
			count++;

	return count == 1;
}

void UlamNumbers(int n) {
	int candidate, i, j;
	vector<int> vI;
	vector<int> vJ;
	vector<int> UlamResult;

	PopulateSieve(sieve, 10000000);

	for (i = 1; i <= 3; i++) {
		vI.push_back(i);
		vJ.push_back(i);
	}

	for (candidate = 4; candidate <= n; candidate++) {

		UlamResult.clear();

		for (i = 0; i < vI.size(); i++) {
			int ui = vI[i];

			for (j = 0; j < vJ.size(); j++) {
				int uj = vJ[j];

				if (ui == uj || uj > ui)
					continue;

				UlamResult.push_back(ui + uj);
			}
		}

		if (CountEqualOne(candidate, UlamResult)) {
			vI.push_back(candidate);
			vJ.push_back(candidate);
		}
	}

	j = 0;

	for (i = 0; i < vI.size(); i++) {
		if (sieve[vI[i]]) {
			cout << setw(4) << vI[i] << ' ';

			if ((j + 1) % 10 == 0) {
				j = 0;
				cout << endl;
			}
			else
				j++;
		}
	}

	cout << endl;
}

int main(int argc, char * const argv[]) {
	clock_t clock0 = clock();

	cout << "Ulam sequence prime numbers < 5000" << endl << endl;
	UlamNumbers(5000);
	clock0 = clock() - clock0;
	cout << endl << endl << "seconds = ";
	cout << (double)clock0 / CLOCKS_PER_SEC << endl;
	return 0;
}