[seqfan] Related to Collatz

Melvin M Peralta melvinmperalta at gmail.com
Tue Feb 16 02:06:06 CET 2016


Hello SeqFans,

a(1) = 1, a(2) = 2
a(n + 1) = floor[sqrt(a(n))], if not already in the sequence
otherwise, a(n + 1) = a(n) + a(n - 1)

It's a bit of Collatz and Fibonacci.

Here are the first few terms:
1, 2, 3, 5, 8, 13, 21, 4, 25, 29, 54, 7, 61, 68, 129, 11, 140, 151

The biggest question is if it's an integer permutation. Thoughts on how to
approach? My guess is there's a good chance, since n will appear if n^2,
n^4, n^8, and so on appear at any point.

Are there too many sequences similar to this one? Worth adding to OEIS or
not interesting enough?

Any other comments or questions that come out of this sequence are welcome!

Best regards,
Melvin



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