Lucas Numbers

[John Hanna]

Puzzling over a problem:

Lucas Numbers are a sequence like Fibonacci Numbers but with any two starting numbers. What's the longest Lucas sequence that contains the number 1,000,000?

Thinking about working backwards from 1,000,000...?

Regards,

    John

[Bert Wikkerink]

I found:

{154,144,298,442,740,1182,1922,3104,5026,8130,13156,21286,34442,55728,90170,145898,236068,381966,618034,1000000}

Just brute force in a Python program

Regards,

Bert

Op 3 jul 2025, om 13:45 heeft John Hanna <johne...@gmail.com> het volgende geschreven:

Puzzling over a problem:

Lucas Numbers are a sequence like Fibonacci Numbers but with any two starting numbers. What's thelongest Lucas sequence that contains the number 1,000,000?

Thinking about working backwards from 1,000,000...?

Regards,

    John

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[John Hanna]

Yeah... 618043/1000000=phi

John Hanna

To view this discussion visit https://groups.google.com/d/msgid/tinspire/A10494EA-B63A-4EBC-9439-9DB006304874%40gmail.com.

[John Hanna]

Let's see the code!

Regards,

    John

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From: tins...@googlegroups.com <tins...@googlegroups.com> on behalf of Bert Wikkerink <b.wik...@gmail.com>
Sent: Thursday, July 3, 2025 2:06 PM
To: tins...@googlegroups.com <tins...@googlegroups.com>
Subject: Re: [tinspire] Lucas Numbers

 

To view this discussion visit https://groups.google.com/d/msgid/tinspire/A10494EA-B63A-4EBC-9439-9DB006304874%40gmail.com.

[Bert Wikkerink]

For the code see below.

(I also included a tns-file) 

Regards,

Bert

# make a list of fibonacci numbers

fib=[1,1]

for i in range(2,31):

  fib.append(fib[i-2]+fib[i-1])

#define a Lucas number

def lucas(a,b,n):

  return fib[n-1]*a+fib[n]*b

#check for different starting numbers a and b the

#lucas numbers less than or equal to 1000000

for a in range(1,1000):

  for b in range(1,1000):

    n=1

    luc=0

    while luc<=1000000:

      luc = lucas(a,b,n)

      if luc == 1000000:

        print(a,b,n+1,luc)

        break

      n = n+1

[John Hanna]

I did something similar but with no results.

John Hanna

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[John Hanna]

Had to tweak the code but found others:

Regards,

    John

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From: John Hanna <johne...@gmail.com>
Sent: Friday, July 4, 2025 8:44 AM
To: tinspire <tins...@googlegroups.com>