[seqfan] Re: Fractions, digits, decimal expansion

[Lars Blomberg]

Hello, 

For A265740 I get
n       a(n)    F(n)
1	1	2
34	2	4
544	4	5
1241	5	50
2539	50	165
2738	165	450
4702	450	1650
10042	1650	1980
19499	1980	2475
35324	2475	24750
50422	24750	24975
59425	24975	59400
59447	59400	59448
59448	59448	59449
59449	59449	59450
...
Continues with stretches of sequential numbers interrupted by smaller or larger jumps.
(Unfortunately there was a mistake in my original data. I have submitted
a correction which has not yet been approved. That is why my values differ slightly.)

For A265756 I get
n       a(n)    F(n)
1	1	2
33	2	4
540	4	5
1236	5	40
4154	40	250
6252	250	1250
6489	1250	1650
10042	1650	1980
19499	1980	2475
35324	2475	24750
50422	24750	24975
59425	24975	59400
59447	59400	59448
59448	59448	59449
59449	59449	59450
...
and a similar continuation as above.

Comparing the two sequences up to nMax there are D(nMax) differences.
Showing also the last difference between the two sequences.
nMax  D(nMax)   D(n)/n      n  A265740 A265756
10^4     7897   0.79     9987     9999    9990
10^5    10644   0.11    99998    99999   99990
10^6    13187   0.013  999998   999999  999990
so the differences certainly become more sparse.
I will try for 10^7 but that is probably still too small.

/Lars B

-----Ursprungligt meddelande-----
Från: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] För Bob Selcoe
Skickat: den 16 december 2015 14:46
Till: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Ämne: [seqfan] Re: Fractions, digits, decimal expansion

Hi Hans, Lars and Seqfans,

Thanks Lars and Hans for posting A265740 and A265756.

Might the two sequences eventually converge?  If so, I imagine n would be large.

It would be interesting to see where the smallest missing term appears in both sequences.  For example A265740; using Lars' terminology, F(n)= smallest missing term up to n:

n         a(n)      F(n)

1           1          2
34         2          4
539       4         5
1239     5        50
2531    50      165
2731   165     ...

Would n and F(n) for both sequences be worth contributing?

Cheers,
Bob S. 


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