G(n) values of Grundy's Game

Info about Grundy's Game: here and here.

Old results (from this page)

Calculated until January 1992: all G(n) with n <= 80*106 which yielded the discovery of 13 new sparse values to the previously 1264 known ones.
Calculated November and December 1993: all G(n) with n <= 502*106.
From August 1995 until March 1996 Dan Hoey computed all values G(n) up to 11*109. All common values up to 287 have occured in this range. The last maximal value is G(4563802297)=291, but no further sparse values appeared.
Calculated in December 2000: all G(n) with n <= 5*232. On average 3130 common values were to check to verify the next "Nim-value candidate" and the farest to-iterate index=16746922727 was 50248198 apart.
Calculated until mid of May 2002: all G(n) with n <= 235 by Achim Flammenkamp.

New results

Our solver uses CUDA to speed up computations. The current version calculates 235 values in about 12 hours.
We do not save all values because of huge number of them; we remember just 228 (about 2.7 * 108) of the first and the last values.
To verify if the sequence has a period we do computations in two steps: first, we calculate all values up to 2k-1 and save 100 the last ones (in table below marked as "calculated"); then we verify whether it has a period during calculating values in range [2k, 2k+1-1] checking if these 100 values appear as substring. No matches mean that there is no period up to 2k-1 (in the table marked as "verified").

Updates

2016-02-25

Created this page.
Calculated all G(n) with n < 239.
No period is found up to this n. No new sparse values.
Maximal depth indices: J[39835365778]=50536776, J[96972674506]=50808031 and J[444030669025]=51335131.

2016-03-13

Calculated all G(n) with n < 240.
New max depth index J[972355516182]=51881350.
New max value G[1084486826694]=303.

2016-04-03

Calculated all G(n) with n < 241.
New max depth index J[1428887192014]=52235263.

nG[n]StatusFiles
[235-100,
235-1]		 
 39  64  99  51  64  99  39  64 112  70  74  53  51  74  50  32  77  38  52  77
 50  70 101  33  65 123  33  65  98  38 139  98  14  70  98  38  75  98  53  65
 51  38  76  52  64 139  51  71  85  32 128  99  32  64 100  32  71  82  22  64
 99  32 141  75  39 123  99  32  74  50  52 138  26  70  64  38 134 124  56  52
 71  33 134  98  33 146  98  33  65  83  50  65  71  38 139  98  53  75  32  38
calculated: 2016-01-03
verified: 2016-01-05
no period		 Frequencies
Sparse values
Maximum values
Depth indices
[236-100,
236-1]		 
128  75  71  22  70  51 128  75  52  17  75  83  17  50  52  17  50  52 128  50
 51  17  14  51  83  14  84  17  63 129  74  50  16  71  53  84  71  53  16  51
 50  70  51  82  70  51  53  15  51  63 129  52  53  75  52  53 112  52  22  76
 51  22 112  62 128  75  52 128  76  52  17  53  57 128  50  51  22  76  57  71
 76  57 118  85  23  17  50  84  74  56  51  74  56  51  77  85  70  71  50  70
calculated: 2016-01-05
verified: 2016-01-08
no period		 Frequencies
Sparse values
Maximum values
Depth indices
[237-100,
237-1]		 
129  26  82 129  26  17 134  32  17 129  32  17 129  39  82  50  39  17  38  51
 82  50  52 128  50  51 128  50  71 128  50  26 128  27  84 128  53  83 128  50
 16 128  50  83  52  53  83  51  50  26  51  56 129  51  53 129  51  76 134  51
 53 129  26  50 129  32  22 134  51  85 134  51  22 129  26  17 129  51  82 134
 52  82  50  83  85  50  83 128  50  51 128  50  83 135  33  52  74  38  16  74
calculated: 2016-01-09
verified: 2016-01-11
no period		 Frequencies
Sparse values
Maximum values
Depth indices
[238-100,
238-1]		 
 83  16 134  51  16  82  52   9  82  83  14  88  57  29  82  15 128  63  51 128
 63  17 128  50  17 125  53  98  83  50   8  29  53   8 153  50  15  83  50  15
 89  50  15  62  53   2  52  16  28  83  56 134  51  14 140  52  14 129  83   9
 82  52  16  82  57  16  85  51  14  82  51   9  82  15  16  88  62  16  82  51
128  56  51  84  63  22 138  82  98  83  53  22  84  53  15  84  63 101  84  53
calculated: 2016-01-13
verified: 2016-01-21
no period		 Frequencies
Sparse values
Maximum values
Depth indices
[239-100,
239-1]		 
138  23  39 147  16  39 141  26 113  32  16  88  32  16 113  17  16 134  32  16
129  32  16  95  22  38  85  27  23  88  17 119 140  17 112  85  22 125 176  17
153  33  17 119  33  17 112  33  17 128  16  22 128  33  32  89  23  17 138  29
 39 138  23  39  89  26 139  74  16 123  32  33  17  32  16 113  39  23 113  39
 23  85  32  23  50  32  23  88  32  16 139  17  33  95  17  89  88  28 165  38
calculated: 2016-01-21
verified: 2016-02-02
no period		 Frequencies
Sparse values
Maximum values
Depth indices
[240-100,
240-1]		 
 22  89  50  17  83  38  17  89  33  17  51  16  17  52  16  22  52  16  17  71
 29  22  51  16 100  51  26  17  51  16  85  64  16  17  51  16  53  39  23  53
 22  23  50  32  16  50  22  84  50  17  16  50  17  16  53  17  16  70  22  71
 56  17  98  50  17  98  50  17  52  38  27  52  33  17  71  16  17  52  16  17
 57  16  22  51  29  99  51  16  88  51  16  88  51  16  88  32  16  65  32  16
calculated: 2016-03-13
verified: 2016-03-31
no period		 Frequencies
Sparse values
Maximum values
Depth indices
[241-100,
241-1]		 
 82  39  38  85  39  38 140  39  98  16  32  98  33  39 138  23  77 138  33 105
 84  16  71 138  33  39 138  33  99  83  23  99  83  38 149  32  38  71  32  76
129  32  44 152  32  98  82  83  70  88  32  38  88  22  75 134  17  43 140  32
128  33  17  98  95  32 141  23  32 141  33  27 141  33  71 141  33  32  83  16
 39  83  33  39 128  33 100  83  16 100  89  33 129  17  38  71  32  43  39  32
calculated: 2016-03-31
verified: ??		 Frequencies
Sparse values
Maximum values
Depth indices
Artem Ripatti (ripatti [cat] inbox [dot] ru), last update: 2016-04-03