# The Lucas Sequence

## 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349

The Lucas numbers unfortunately aren’t as famous as they should be but many would still recognize it’s rule from a more popular sequence called the Fibonacci sequence. Same rule as the Fibonacci sequence only the start is switched from 1, 1, to 2, 1. Any two numbers that you apply this rule to the ratio of the numbers will get you a closer and closer approximation to Phi Φ.

Lucas Numbers in blue

1. 1
2. 3
3. 4
4.  — 7
5.  — 11
6. 18
7. —  29
8. 47
9. 76
10. 123
11. 199
12. 322
13. 521
14. 843
15. 1364
16. 2207
17. 3571
18. 5778
19. 9349

## Lucas Number and φ

2/1= 1

3/2= 1.5

4/3= 1.3333 —

7/4= 1.75

11/7= 1.57142857

18/11= 1.63636364

29/18= 1.611111 —

47/29= 1.62068

76/47= 1.61702128

123/76= 1.61842105

199/123= 1.61788618

322/199= 1.61809045

Every power of Phi rounded to the nearest whole number will give you a Lucas number..

# The first 20 Primes in the Lucas Numbers

— 6 of the first 9 Lucas numbers are prime.

— 10 primes are found within the first 20 Lucas numbers.

That’s a lot of primes close together!

Primes in purple

# 521, 843, 1364, 2207, 3571, 5778, 9349

3571 is the 500th prime number and the 70th from 3001-4000.

# EVEN ODD ODD EVEN ODD ODD

## Primes in the Fibonacci sequence

— 3 primes within the first 9 numbers.

— 6 primes within the first 20 numbers.