[seqfan] Re: Sequence related to Collatz 3n+1

[Neil Sloane]

I think that is interesting and worth adding to the OEIS - please do so!
Neil

On Fri, Mar 29, 2013 at 6:37 PM, DAN_CYN_J <dan_cyn_j at comcast.net> wrote:

>
>
> Hi all seq. fans.
>
> In Collatz 3n+1 conjecture the first and following
> seeds that have an integer divisor of its total
> sequence sum. This sum and level (sequence count)
> includes the seed.
>
> This unique seed sequence with this property =
> 1,57,847,1694,3039,3388,3479,6078,6776,6958,13916,27832,55664,111328,236107,246721
> ...
>
>
>
> This sequence is not in OEIS.
>
>
>
> Explaining it further below.
>  1,4,2,1 = level 4,seed 1 and sum 8 of total sequence and divisor 8.
> (8*1)=sum 8
>  57..4,2,1 =level 33,seed 57 and sum 1653 of total sequence and divisor
> 29. (29*57)= sum 1653
>  847..4,2,1 =level 34,seed 847 and sum 49126 and divisor 58. (58*847)= sum
> 49126
>  etc.
>
> The associated table for each seed.
>
> Level |seed     | sum        | divisor
>   4      | 1           |  8            | 8
> -----------------------------
>  33    | 57        |  1653       | 29
> -----------------------------
>  34   | 847      | 49126      | 58
> -----------------------------
>  35   | 1694   | 50820      | 30
> -----------------------------
>  155  | 3039   | 449772   | 148
> -----------------------------
>  36   | 3388   | 54208     | 16
> -----------------------------
>  57   | 3479   | 118286   |  34
> -----------------------------
>  156  | 6078   | 455850   |  75
> -----------------------------
>  37   | 6776   | 60984     |  9
> -----------------------------
>  58   | 6958   | 125244    |  18
> -----------------------------
>  59   | 13916  | 139160    |  10
> -----------------------------
>  60   | 27832  | 166992    |  6
> -----------------------------
>  61   | 55664  | 222656    |  4
> -----------------------------
>  62   | 111328 | 333984   |  3
> -----------------------------
>  50   | 236107 | 4958247  |  21
> -----------------------------
>  151  | 246721 | 4440978  |  18
> -----------------------------
>  172  | 311257 | 5602626  |  18
> -----------------------------
>  152  | 493442 | 4934420  |  10
> -----------------------------
>  173  | 622514 | 6225140  |  10
> -----------------------------
>  153  | 986884 | 5921304  |  6
> -----------------------------
>  174  |1245028 | 7470168  |  6
> -----------------------------
>  143  |1328233 | 63755184 | 48
> -----------------------------
>  154  |1973768 | 7895072  |  4
> -----------------------------
>  190  |2052521 | 340718486|  166
> ------------------------------
>  175  |2490056 | 9960224   |  4
> ------------------------------
>  144  |2656466 | 66411650  | 25
> ------------------------------
>  155  |3947536 | 11842608  | 3
> ------------------------------
>  191  |4105042 | 344823528 | 84
> ------------------------------
>  176  |4980112 | 14940336  | 3
> ------------------------------
>  192  |8210084 | 353033612 | 43
> ...
> The sums and levels and divisors are all over the place
> within this table but the associated seeds are in sequence.
> So far there are only two discrete prime divisors of the sums. (3,29).
> There is only one duplicate of a level so far =(155)
>
> Some of the levels that are in sequence are also
> interesting such as  level 57,58,59,60,61,62.
> The associated divisors are 34,18,10,6,4,3
> The gap in these divisors are 16,8,4,2,1 giving the
> Collatz terminating sequence.
> Another level sequence that is also interesting
> (151,152,153,154,155)
> with gaps  = (8,4,2,1) of their associated divisors =(18,10,6,4,3)
> Another is --
> (172,173,174,175,176)
>
>
>
> It appears there will be many of these sequential level sets
> but I am not sure if the limit will only be (6) as with levels (57->62).
> If any divisor is odd that ends that level sequence or there
> is only one level with that one odd divisor.
>
>
>
> The gaps between seeds get larger and larger in this discrete sequence.
>
>
>
> Probably not interesting enough for OEIS?
>
>
>
> Dan
>
>
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>
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>



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Neil J. A. Sloane, President, OEIS Foundation
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