Hofstadteriana with primes

[Jacques Tramu]

>>
>> From: "Eric Angelini" <Eric.Angelini at kntv.be>
>>> S = 1   3   8   15  26  39  56  75  98  127  158  195  236  279
>> 326...
>>> d =   2   5   7   11  13  17  19  23  29   31   37   41   43   47 ...
>>>
>>> - start S with 1
>>> - add the smallest prime not yet added and not already present in S
>>>
>>> Question:
>>> - What could be the ratio primes/composites of S?
>>

Values of n, S(n),  np=# of primes, ratio = np/n  (%)
10000   497496444       551     5.5100000000
20000   2141711486      1009    5.0450000000
30000   5017893540      1450    4.8333333333
40000   9171756070      1883    4.7075000000
50000   14633885346     2321    4.6420000000
60000   21430427302     2743    4.5716666667
70000   29579575168     3120    4.4571428571
80000   39099128304     3560    4.4500000000
90000   50005773422     3944    4.3822222222
100000  62306400394     4359    4.3590000000
110000  76018199368     4741    4.3100000000
120000  91146222710     5142    4.2850000000
130000  107705970182    5518    4.2446153846
140000  125704424684    5938    4.2414285714
150000  145143091716    6337    4.2246666667
160000  166032781410    6716    4.1975000000
170000  188382597590    7078    4.1635294118
180000  212202960934    7476    4.1533333333
190000  237496708520    7858    4.1357894737
200000  264265658660    8284    4.1420000000
210000  292516109118    8662    4.1247619048
220000  322257377980    9051    4.1140909091
230000  353493546004    9429    4.0995652174
240000  386218953066    9804    4.0850000000
250000  420449172598    10170   4.0680000000
260000  456197076110    10552   4.0584615385
270000  493452644270    10948   4.0548148148
280000  532221632092    11317   4.0417857143
290000  572510955072    11701   4.0348275862
300000  614323472488    12071   4.0236666667

As Frank explained  (thanks to him)  the ratio certainly converges to 0 
(order 1/log(n)) .

A VERY  good approximation of the ratio between 10000 and 300000 is  1/(  2 
* log(n) ) .
In this range  |ratio -  1/(2*log(n))|   <     1/1000

Best regards,

JT.

--------------------------------------
http://www.echolalie.com
--------------------------------------





Hello Seqfans,

I am making a webpage about sequences. I have a lot of sequence examples there. Most of them are in OEIS, but I have several that are not. The sequences themselves are not very interesting (they could be used as puzzle sequences for kids). Without my page I wouldn't submit them. Does the existence of my page change the level of interestingness of these sequences?

Also, for aesthetic reasons it would be nice for me to have every sequence referenced. Is this a good reason to submit?

Best, Tanya


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Can this be related?

http://www.cut-the-knot.org/blue/div7-11-13.shtml

--------- Original Message ----------------------------------

>
>----- Original Message ----- 

>>> > Additional elements:
>>> >
>>> > 0 56 147 238 329 560 651 742 798 833 889 924 1001 1057 1148 1239 1470
>>>
>>> > 1561 1652 1743 1799 1834 1925 2002 2058 2149 2380 2471 2562 2653 2744
>>>
>>> Well, the 1st differences so far consist of a sequence containing
>>> only the numbers 7*5, 7*8, 7*11, 7*13, and 7*33.
>>>



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My favorite example:

A005101  	 	 Abundant numbers 

Start the same as even abundant numbers. The first odd abundant number is 945.

Tanya

---------- Original Message ----------------------------------

>
>Hello SeqFans,
>
>I'm looking for two sequences in the OEIS which have
>their 50 first terms identical -- they would diverge
>afterwards. 
>
>Best,
>É.
>
> 
>
>



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