Pan base non-primes: Difference between revisions
Added C++ solution
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Number odd = 161 or 16.894019%
Number even = 792 or 83.105981%
</pre>
=={{header|C++}}==
<syntaxhighlight lang="cpp">#include <algorithm>
#include <cassert>
#include <cstdint>
#include <iomanip>
#include <iostream>
#include <numeric>
#include <vector>
bool is_prime(uint64_t n) {
if (n < 2)
return false;
if (n % 2 == 0)
return n == 2;
if (n % 3 == 0)
return n == 3;
if (n % 5 == 0)
return n == 5;
static constexpr uint64_t wheel[] = {4, 2, 4, 2, 4, 6, 2, 6};
for (uint64_t p = 7;;) {
for (uint64_t w : wheel) {
if (p * p > n)
return true;
if (n % p == 0)
return false;
p += w;
}
}
}
std::vector<uint64_t> digits(uint64_t n) {
std::vector<uint64_t> d;
for (uint64_t m = n; m > 0; m /= 10)
d.push_back(m % 10);
reverse(d.begin(), d.end());
return d;
}
template <typename iterator> auto gcd(iterator begin, iterator end) {
assert(begin != end);
auto result = *begin++;
for (; begin != end; ++begin)
result = std::gcd(result, *begin);
return result;
}
template <typename number, typename iterator>
number polyval(iterator begin, iterator end, number value) {
number n = 0;
for (auto i = begin; i != end; ++i)
n = n * value + *i;
return n;
}
bool is_pan_base_non_prime(uint64_t n) {
if (n < 10)
return !is_prime(n);
if (n > 10 && n % 10 == 0)
return true;
auto d = digits(n);
if (gcd(d.begin(), d.end()) > 1)
return true;
auto max_digit = *std::max_element(d.begin(), d.end());
for (uint64_t base = max_digit + 1; base <= n; ++base) {
if (is_prime(polyval(d.begin(), d.end(), base)))
return false;
}
return true;
}
int main() {
std::vector<uint64_t> pbnp;
const uint64_t limit = 10000;
for (uint64_t n = 2; n <= limit; ++n) {
if (is_pan_base_non_prime(n))
pbnp.push_back(n);
}
std::cout << "First 50 pan-base composites:\n";
for (size_t i = 0; i < 50; ++i) {
std::cout << std::setw(3) << pbnp[i]
<< ((i + 1) % 10 == 0 ? '\n' : ' ');
}
std::cout << "\nFirst 20 odd pan-base composites:\n";
for (size_t i = 0, count = 0; count < 20; ++i) {
if (pbnp[i] % 2 == 1) {
++count;
std::cout << std::setw(3) << pbnp[i]
<< (count % 10 == 0 ? '\n' : ' ');
}
}
size_t total = pbnp.size();
size_t odd = std::count_if(pbnp.begin(), pbnp.end(),
[](uint64_t n) { return n % 2 == 1; });
std::cout << "\nCount of pan-base composites up to and including " << limit
<< ": " << total << '\n';
auto percent = (100.0 * odd) / total;
std::cout << std::fixed;
std::cout << "Percent odd up to and including " << limit << ": " << percent
<< '\n';
std::cout << "Percent even up to and including " << limit << ": "
<< 100.0 - percent << '\n';
}</syntaxhighlight>
{{out}}
<pre>
First 50 pan-base composites:
4 6 8 9 20 22 24 26 28 30
33 36 39 40 42 44 46 48 50 55
60 62 63 64 66 68 69 70 77 80
82 84 86 88 90 93 96 99 100 110
112 114 116 118 120 121 130 132 134 136
First 20 odd pan-base composites:
9 33 39 55 63 69 77 93 99 121
143 165 169 187 231 253 273 275 297 299
Count of pan-base composites up to and including 10000: 3849
Percent odd up to and including 10000: 18.030657
Percent even up to and including 10000: 81.969343
</pre>
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