[seqfan] Re: Fractions, digits, decimal expansion
Lars Blomberg
larsl.blomberg at comhem.se
Tue Dec 15 16:39:44 CET 2015
Hello,
Maybe I am misunderstanding something, but I find a(63)=9.
1
6 0.1(6)
13 0.(461538)
10 1.3(0)
14 0.(714285)
17 0.(8235294117647058)
7 2.(428571)
8 0.875(0)
19 0.(421052631578947368)
23 0.(8260869565217391304347)
21 1.0(952380)
29 0.(7241379310344827586206896551)
34 0.8(5294117647058823)
31 1.0(967741935483870)
3 10.(3)
38 0.0(789473684210526315)
28 1.3(571428)
46 0.(6086956521739130434782)
47 0.(9787234042553191489361702127659574468085106382)
35 1.3(428571)
39 0.(897435)
49 0.(795918367346938775510204081632653061224489)
43 1.(139534883720930232558)
51 0.(8431372549019607)
42 1.2(142857)
41 1.0(24390)
48 0.8541(6)
53 0.(9056603773584)
26 2.0(384615)
12 2.1(6)
57 0.(210526315789473684)
58 0.9(8275862068965517241379310344)
59 0.(9830508474576271186440677966101694915254237288135593220338)
2 29.5(0)
61 0.0(327868852459016393442622950819672131147540983606557377049180)
24 2.541(6)
68 0.(3529411764705882)
11 6.(18)
52 0.21(153846)
63 0.(825396)
22 2.8(63)
69 0.(3188405797101449275362)
62 1.1(129032258064516)
71 0.(87323943661971830985915492957746478)
56 1.267(857142)
65 0.8(615384)
76 0.85(526315789473684210)
81 0.(938271604)
44 1.84(09)
67 0.(656716417910447761194029850746268)
64 1.046875(0)
83 0.(77108433734939759036144578313253012048192)
85 0.9(7647058823529411)
78 1.0(897435)
77 1.0(129870)
79 0.(9746835443037)
72 1.097(2)
84 0.(857142)
86 0.(976744186046511627906)
87 0.(9885057471264367816091954022)
80 1.0875(0)
89 0.(89887640449438202247191011235955056179775280)
9 9.(8)
As to the question of the sequence being a permutation,
the following table shows:
C=Number of terms calculated
F=First term that is missing
C F F/C
1000 5 0.005
2000 50 0.025
5000 1480 0.296
10000 1650 0.165
20000 2475 0.124
50000 24750 0.495
100000 83250 0.833
200000 198000 0.990
500000 495000 0.990
which seems to support the conjecture.
/Lars
-----Ursprungligt meddelande-----
Från: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] För Hans Havermann
Skickat: den 15 december 2015 14:19
Till: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Ämne: [seqfan] Re: Fractions, digits, decimal expansion
Bob Selcoe:
> I may have spoken too soon: 80190/9 = 8910. It may be impossible for
> S to equal 80190 or another "precursor" of 9 but I'm not so sure.
>
> Perhaps someone who knows how to program could expand the sequence and
> see if 9 appears?
A no-leading-or-trailing-zeros version of the sequence has 9 appearing after 89, earlier than the appearances of either 4 or 5. Allowing the leading and trailing zeros makes the sequence *less* constrained.
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