with

and . The th Lucas number is imposed in the rebab.net Language together LucasLYou are watching: 1 3 4 7 11 18 29

The worths of

because that , 2, ... Room 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, ... (OEIS A000204).The Lucas numbers are additionally a Lucas succession

and also are the companions come the Fibonacci number and also satisfy the very same recurrence.The number of ways of picking a collection (including the north set) indigenous the numbers 1, 2, ...,

without picking 2 consecutive numbers (where 1 and also are now consecutive) is (Honsberger 1985, p.122).The only square numbers in the Lucas sequence room 1 and also 4 (Alfred 1964, Cohn 1964). The only triangular Lucas numbers room 1, 3, and also 5778 (Ming 1991). The just cubic Lucas number is 1.

Rather amazingly, if

is prime, . The converse does no necessarily hold true, however, and composite number such the are known as Lucas pseudoprimes.For

, 2, ..., the number of decimal digits in (OEIS A097348), where is the golden ratio. This adheres to from the fact that for any type of power function , the number of decimal digits because that is provided by .See more: What Is The State Bird Of Oregon? Oregon State Bird

The lengths the the cycles because that Lucas numbers (mod

) for , 2, ... Are 12, 60, 300, 3000, 30000, 300000, 300000, ... (OEIS A114307).