Vampire number
Vampire number is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
A Vampire number is a natural number with an even number of digits, that can be factored into two integers. These 2 factors are called the fangs, and must have the following properties:
- they each have half the number of the digits of the orginal number
- together they consist of exactly the same digits as the orginal number
- at most one of them has a trailing zero
An example of a Vampire number and its fangs: 1260 : (21, 60)
Task description:
- Print the first 25 Vampire numbers and their fangs.
- Check if the following numbers are vampire numbers and, if so, print them and their fangs:
16758243290880, 24959017348650, 14593825548650
Note that a Vampire number can have more than 1 pair of fangs.
Cf:
D
<lang d>import std.stdio, std.algorithm;
void main() {
for (long n, count; n < 250_000L && count < 25; n++)
if (auto factors = vampireNumberFactors(n)) {
writefln("%s : %(%s %)", n, factors);
count++;
}
writeln();
foreach (n; [16758243290880L, 24959017348650L, 14593825548650L])
if (auto factors = vampireNumberFactors(n))
writefln("%s : %(%s %)", n, factors);
}
long[2][] vampireNumberFactors(in long n) {
long[2][] factorPairs(in long k) pure {
typeof(return) res;
foreach (i; 2 .. cast(long) (k ^^ 0.5 + 1)) {
if (k % i == 0) {
long q = k / i;
if (q > i)
res ~= [i, q];
}
}
return res;
}
long[] getDigits(in long k) pure {
typeof(return) digits;
long m = k;
while (m > 0) {
digits ~= (m % 10);
m /= 10;
}
return digits.reverse;
}
if (n < 2) return null;
typeof(return) result;
auto digits = getDigits(n).sort().release();
if (digits.length & 1)
return null;
immutable half = digits.length / 2;
foreach (pair; factorPairs(n)) {
auto f1 = getDigits(pair[0]);
if (f1.length != half)
continue;
auto f2 = getDigits(pair[1]);
if (f2.length != half)
continue;
if (f1[$-1] == 0 && f2[$-1] == 0)
continue;
if (digits != (f1 ~ f2).sort().release())
continue;
result ~= pair; } return result;
}</lang>
- Output:
1260 : [21, 60] 1395 : [15, 93] 1435 : [35, 41] 1530 : [30, 51] 1827 : [21, 87] 2187 : [27, 81] 6880 : [80, 86] 102510 : [201, 510] 104260 : [260, 401] 105210 : [210, 501] 105264 : [204, 516] 105750 : [150, 705] 108135 : [135, 801] 110758 : [158, 701] 115672 : [152, 761] 116725 : [161, 725] 117067 : [167, 701] 118440 : [141, 840] 120600 : [201, 600] 123354 : [231, 534] 124483 : [281, 443] 125248 : [152, 824] 125433 : [231, 543] 125460 : [204, 615] [246, 510] 125500 : [251, 500] 16758243290880 : [1982736, 8452080] [2123856, 7890480] [2751840, 6089832] [2817360, 5948208] 24959017348650 : [2947050, 8469153] [2949705, 8461530] [4125870, 6049395] [4129587, 6043950] [4230765, 5899410]