[seqfan] Collatz-like algorithm with Fibonacci numbers, Octagonal numbers, Octagonal pyramidal numbers, and Hexagonal numbers.

[Ali Sada]

Hi Everyone,

 

I tried theCollatz-like algorithms we used in A326825 and A326923 with Fibonacci numbers, Octagonalnumbers, Octagonal pyramidal numbers, and Hexagonal numbers with similarresults. The algorithm terminates at certain numbers whether we use the forwardversion (e.g. smallest octagonal number > k) or the backward version (e.g. largestoctagonal number < k.) 

 

The initial resultsare:

 

With the Fibonaccinumbers, the forward algorithm terminates at either 1 or 5.

With the Fibonaccinumbers, the backward algorithm terminates at 1. 

With Octagonalnumbers, the forward algorithm terminates at either 5 or 9 (some 9 circles passthrough 1.)

With the Octagonalnumbers, the backward algorithm terminates at 1.

With the Octagonalpyramidal numbers, the forward algorithm terminates at 1 or 23.

With the Octagonalpyramidal numbers, the backward algorithm terminates at 1 or 35.

With the Hexagonalnumbers, the forward algorithm terminates at 3, 7 or 19.

With the Hexagonalpyramidal numbers, the backward algorithm terminates at 1 or 9.

 
I have tosay here that these results came from a small amount of data.   
 

My questionis: should sequences similar to A326825 be added to the OEIS, or am I overusingthe idea?

 

Best,

 

Ali