# 1. ## Lucas Number

The Lucas numbers or Lucas series are an integer sequence named after the mathematician François Édouard Anatole Lucas (1842–91), who studied both that sequence and the closely related Fibonacci numbers. Lucas numbers and Fibonacci numbers form complementary instances of Lucas sequences.

## Lucas number - Wikipedia

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2. ## Lucas number - Wikipedia

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The Lucas numbers or Lucas series are an integer sequence named after the mathematician François Édouard Anatole Lucas (1842–91), who studied both that sequence and the closely related Fibonacci numbers. Lucas numbers and Fibonacci numbers form complementary instances of Lucas sequences.
The Lucas sequence has the same recursive relationship as the Fibonacci sequence, where each term is the sum of the two previous terms, but with different starting values. This produces a sequence where t…

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3. ## Lucas Number -- from Wolfram MathWorld

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The only square numbers in the Lucas sequence are 1 and 4 (Alfred 1964, Cohn 1964). The only triangular Lucas numbers are 1, 3, and 5778 (Ming 1991). The only cubic Lucas number is 1. Rather amazingly, if is prime, . The converse does not necessarily hold true, however, and composite numbers such that are known as Lucas pseudoprimes.

4. ## Lucas Numbers - GeeksforGeeks

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Nov 17, 2016 · Lucas numbers are similar to Fibonacci numbers. Lucas numbers are also defined as the sum of its two immediately previous terms. But here the first two terms are 2 and 1 whereas in Fibonacci numbers the first two terms are 0 and 1 respectively.

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5. ## The Lucas Numbers - University of Surrey

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The Lucas numbers or Lucas series, and their fascinating connections with the Fibonacci numbers and the golden section. The first 200 Lucas numbers, and lots of investigations and You do the maths... to find your own formulas and patterns in the series. For schools, teachers, colleges and university level students or just for recreation!

6. ## Lucas number的圖片

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7. ## The first 200 Lucas Numbers - University of Surrey

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and here is the output - a table of the first 200 Lucas numbers and their factors, where the prime numbers are indicated: ... To help with your investigations, here are the results of a search for prime number among the first 1000 Lucas numbers: The only Lucas number which …

8. ## Lucas Numbers | Brilliant Math & Science Wiki

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The Lucas numbers or Lucas series are an integer sequence named after the mathematician François Édouard Anatole Lucas (1842–91), who studied both that sequence and the closely related Fibonacci numbers. Similar to the Fibonacci numbers, each Lucas number is defined to be the sum of its two immediately previous terms. However, unlike the Fibonacci numbers, which start as ...

9. ## Lucas number : definition of Lucas number and synonyms of ...

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• Like the Fibonacci numbers, each Lucas number is defined to be the sum of its two immediate previous terms, i.e. it is a Fibonacci integer sequence. Consequently, the ratio between two consecutive Lucas numbers converges to the golden ratio. However, the first two Lucas numbers are L0 = 2 and L1 = 1 instead of 0 and 1, and the properties of Lucas numbers are therefore somewhat different from those of Fibonacci numbers.A Lucas number may thus be defined as follows:The sequence of Lucas numbers...
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10. ## The Top Twenty: Lucas Number

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A Lucas prime is a Lucas number that is prime. Recall that the Lucas numbers can be defined as follows: v 1 = 1, v 2 = 3 and v n+1 = v n + v n-1 (n > 2) It can be shown that, for odd m, v n divides v nm. Hence, for v n to be a prime, the subscript n must be a prime, a power of 2, or zero. However, a prime or power of 2 subscript is not sufficient!