d269909faa
* fix: clean-up Project Euler 381-400 * fix: missing image extension * fix: missing subscripts Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
59 lines
1.5 KiB
Markdown
59 lines
1.5 KiB
Markdown
---
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id: 5900f4f11000cf542c510003
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title: 'Problem 387: Harshad Numbers'
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challengeType: 5
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forumTopicId: 302051
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dashedName: problem-387-harshad-numbers
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---
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# --description--
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A Harshad or Niven number is a number that is divisible by the sum of its digits.
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201 is a Harshad number because it is divisible by 3 (the sum of its digits.)
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When we truncate the last digit from 201, we get 20, which is a Harshad number.
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When we truncate the last digit from 20, we get 2, which is also a Harshad number.
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Let's call a Harshad number that, while recursively truncating the last digit, always results in a Harshad number a right truncatable Harshad number.
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Also:
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$\frac{201}{3} = 67$ which is prime.
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Let's call a Harshad number that, when divided by the sum of its digits, results in a prime a strong Harshad number.
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Now take the number 2011 which is prime. When we truncate the last digit from it we get 201, a strong Harshad number that is also right truncatable. Let's call such primes strong, right truncatable Harshad primes.
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You are given that the sum of the strong, right truncatable Harshad primes less than 10000 is 90619.
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Find the sum of the strong, right truncatable Harshad primes less than ${10}^{14}$.
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# --hints--
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`harshadNumbers()` should return `696067597313468`.
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```js
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assert.strictEqual(harshadNumbers(), 696067597313468);
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```
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# --seed--
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## --seed-contents--
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```js
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function harshadNumbers() {
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return true;
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}
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harshadNumbers();
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```
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# --solutions--
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```js
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// solution required
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```
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