47 lines
1.2 KiB
Markdown
47 lines
1.2 KiB
Markdown
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---
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id: 5900f4931000cf542c50ffa4
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title: 'Problem 293: Pseudo-Fortunate Numbers'
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challengeType: 5
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forumTopicId: 301945
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dashedName: problem-293-pseudo-fortunate-numbers
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---
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# --description--
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An even positive integer $N$ will be called admissible, if it is a power of 2 or its distinct prime factors are consecutive primes.
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The first twelve admissible numbers are 2, 4, 6, 8, 12, 16, 18, 24, 30, 32, 36, 48.
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If $N$ is admissible, the smallest integer $M > 1$ such that $N + M$ is prime, will be called the pseudo-Fortunate number for $N$.
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For example, $N = 630$ is admissible since it is even and its distinct prime factors are the consecutive primes 2, 3, 5 and 7. The next prime number after 631 is 641; hence, the pseudo-Fortunate number for 630 is $M = 11$. It can also be seen that the pseudo-Fortunate number for 16 is 3.
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Find the sum of all distinct pseudo-Fortunate numbers for admissible numbers $N$ less than ${10}^9$.
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# --hints--
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`pseudoFortunateNumbers()` should return `2209`.
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```js
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assert.strictEqual(pseudoFortunateNumbers(), 2209);
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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 pseudoFortunateNumbers() {
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return true;
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}
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pseudoFortunateNumbers();
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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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