Statistics on golden ratio digits
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These statistics were obtained with the 17 000 000 000 first digits of the golden ratio.
Detailed frequences
Individual digits
Number of occurences of each digit
(expected number if φ is normal : 1 700 000 000)
0 : 1 700 032 820
1 : 1 699 962 967
2 : 1 699 965 930
3 : 1 700 009 433
4 : 1 699 996 976
5 : 1 700 000 305
6 : 1 700 011 260
7 : 1 700 026 313
8 : 1 700 025 720
9 : 1 699 968 276
total : 17 000 000 000
2-digit sequences
Number of occurences of each 2-digit sequence
(expected number if φ is normal : 170 000 000)
00 170016807
01 169999745
02 170015823
03 170009365
04 169981832
05 170002206
06 170018053
07 169986020
08 169997371
09 170005598
10 169988944
11 170006452
12 169982967
13 169983915
14 170002700
15 169990235
16 169992761
17 170005460
18 170000376
19 170009157
20 169989631
21 169987490
22 170003750
23 169994916
24 169993253
25 170014278
26 169997379
27 170011318
28 169999260
29 169974655
30 170005999
31 170003199
32 169994898
33 170007262
34 169996074
35 169991163
36 169998833
37 170010962
38 170005210
39 169995833
40 169996800
41 170016563
42 170006830
43 169991223
44 169992774
45 170004471
46 170009567
47 170009513
48 169983273
49 169985962
50 170026352
51 169975912
52 169983720
53 169999896
54 170008727
55 169978785
56 170001390
57 170002436
58 170012036
59 170011051
60 170006424
61 169988560
62 170001462
63 169999001
64 170002812
65 170013399
66 169992457
67 169998371
68 170009578
69 169999196
70 169994872
71 170004283
72 169990044
73 170009401
74 170006435
75 170013913
76 170005778
77 169993632
78 170006267
79 170001688
80 170014917
81 169990346
82 170000180
83 170005034
84 169997367
85 169994767
86 170013798
87 170004773
88 170015857
89 169988681
90 169992074
91 169990417
92 169986256
93 170009420
94 170015002
95 169997088
96 169981244
97 170003828
98 169996492
99 169996455
Total : 17000000000
Statistics by sequence size
Sequences of size 1:
Most frequent: 0 (1700032820 times)
Less frequent: 1 (1699962967 times)
Standard deviation: 24889.097
(expected value if φ is normal, between 9355 and 54520)
Sequences of size 2:
Most frequent: 50 (170026352 times)
Less frequent: 29 (169974655 times)
Standard deviation: 10399.859
(expected value if φ is normal, between 10976 and 14701)
Sequences of size 3:
Most frequent: 081 (17014079 fois)
Less frequent: 515 (16986993 fois)
Standard deviation: 3929.341
(expected value if φ is normal, between 3933 and 4301)
Sequences of size 4:
Most frequent: 0604 (1705124 fois)
Less frequent: 9844 (1695221 fois)
Standard deviation: 1291.162
(expected value if φ is normal, between 1285.3 and 1322.0)
Sequences of size 5:
Most frequent: 39957 (171755 fois)
Less frequent: 34172 (168293 fois)
Standard deviation: 412.282
(expected value if φ is normal, between 410.461 and 414.148)
Sequences of size 6:
Most frequent: 157806 (17585 fois)
Less frequent: 229443 (16303 fois)
Standard deviation: 130.243
(expected value if φ is normal, between 130.200 and 130.568)
Sequences of size 7:
Most frequent: 5060476 (1928 fois)
Less frequent: 9437813 (1484 fois)
Standard deviation: 41.2245
(expected value if φ is normal, between 41.2127 and 41.2494)
Sequences of size 8:
Most frequent: 05989513 (247 fois)
Less frequent: 38718571 (98 fois)
Standard deviation: 13.03665
(expected value if φ is normal, between 13.03657 and 13.04024)
Sequences of size 9:
Most frequent: 010300471 (49 fois)
Less frequent: 032975181 (0 fois)
Standard deviation: 4.123012
(expected value if φ is normal, between 4.122922 and 4.123290)
Sequences of size 10:
Most frequent: 1376488688 (15 fois)
Less frequent: 0000000011 (0 fois)
Standard deviation: 1.3038370
(expected value if φ is normal, between 1.3038221 and 1.3038589)