Cracking the Sequence: Solving the Mystery of 4,9,50,147,605,1352,3757...

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The sequence 4, 9, 50, 147, 605, 1352, 3757 is identified as a product involving the Fibonacci sequence and the squares of prime numbers. Each term corresponds to a Fibonacci number multiplied by the square of a prime, specifically following the pattern of 1.2^2, 1.3^2, 2.5^2, and so on. Participants in the discussion express their thoughts on the complexity of the sequence and its relation to prime factorization. The connection to Fibonacci numbers is emphasized as a key insight that enhances understanding of the sequence. Overall, the discussion highlights the intriguing mathematical relationship between Fibonacci numbers and prime squares.
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4,9,50,147,605,1352,3757,...

It's not as stupid as the monster group :biggrin:
 
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micromass said:
4,9,50,147,605,1352,3757,...

It's not as stupid as the monster group :biggrin:

For the record, I don't think the monster group is stupid--that's silly--but I would never have remembered the prime factors of its order, ordered first by decreasing powers and then by increasing magnitude.
 
micromass said:
4,9,50,147,605,1352,3757,...

It's not as stupid as the monster group :biggrin:

What is it? I haven't figured it out.
 
The sequence is 1.2^2,1.3^2,2.5^2,3.7^2,5.11^2,8.13^2,13.17^2,...<br /> <br /> So it&#039;s a product with the Fibonacci sequence and the squares of primes...
 
micromass said:
The sequence is 1.2^2,1.3^2,2.5^2,3.7^2,5.11^2,8.13^2,13.17^2,...<br /> <br /> So it&#039;s a product with the Fibonacci sequence and the squares of primes...
<br /> <br /> Ahh, okay. I had looked at the prime decompositions, and noticed the progressing squared primes, but the Fibonacci part didn&#039;t click.
 

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