Increasing gaps between consecutive Niven numbers: Difference between revisions

Content added Content deleted
(Added C++ solution)
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:*   [https://cs.uwaterloo.ca/journals/JIS/VOL6/Doyon/doyon.pdf (PDF) version of the (above) article by Doyon].
:*   [https://cs.uwaterloo.ca/journals/JIS/VOL6/Doyon/doyon.pdf (PDF) version of the (above) article by Doyon].
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=={{header|C++}}==
<lang cpp>#include <cstdint>
#include <iomanip>
#include <iostream>

// Returns the sum of the digits of n given the
// sum of the digits of n - 1
uint64_t digit_sum(uint64_t n, int sum)
{
++sum;
while (n > 0 && n % 10 == 0)
{
sum -= 9;
n /= 10;
}
return sum;
}

int main()
{
// Print numbers with commas
std::cout.imbue(std::locale(""));

uint64_t previous = 1, gap = 0;
int niven_index = 0, gap_index = 1, sum = 0;

std::cout << "Gap index Gap Niven index Niven number\n";
for (uint64_t niven = 1; gap_index <= 32; ++niven)
{
sum = digit_sum(niven, sum);
if (niven % sum == 0)
{
if (niven > previous + gap)
{
gap = niven - previous;
std::cout << std::setw(9) << gap_index++
<< std::setw(5) << gap
<< std::setw(15) << niven_index
<< std::setw(16) << previous << '\n';
}
previous = niven;
++niven_index;
}
}
return 0;
}</lang>

{{out}}
<pre>
Gap index Gap Niven index Niven number
1 1 1 1
2 2 10 10
3 6 11 12
4 7 26 63
5 8 28 72
6 10 32 90
7 12 83 288
8 14 102 378
9 18 143 558
10 23 561 2,889
11 32 716 3,784
12 36 1,118 6,480
13 44 2,948 19,872
14 45 4,194 28,971
15 54 5,439 38,772
16 60 33,494 297,864
17 66 51,544 478,764
18 72 61,588 589,860
19 88 94,748 989,867
20 90 265,336 2,879,865
21 99 800,054 9,898,956
22 108 3,750,017 49,989,744
23 126 6,292,149 88,996,914
24 135 44,194,186 689,988,915
25 144 55,065,654 879,987,906
26 150 61,074,615 989,888,823
27 153 179,838,772 2,998,895,823
28 192 399,977,785 6,998,899,824
29 201 497,993,710 8,889,999,624
30 234 502,602,764 8,988,988,866
31 258 547,594,831 9,879,997,824
32 276 1,039,028,518 18,879,988,824
</pre>


=={{header|Go}}==
=={{header|Go}}==
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