minimale Vorperioden- und Periodenl"angen der Zeilen(Spalten) mit Index < 132 der Sprague-Grundy-funktion g(i,j) f"ur Wythoff's Game ------------------------------------------------------------------------------- i v p max min s 0 0 1 * 0 0 1 0 3 * 1 -2 9 -------- 2 0 3 0 -1 10 -------- 3 8 6 * 3 -4 25 1.892789 4 9 12 * 3 -5 44 1.584963 5 27 24 * 3 -7 98 2.047819 6 37 12 * 4 -8 108 2.015292 7 92 24 * 5 -10 163 2.323740 8 102 24 6 -11 173 2.224142 9 127 24 7 -6 198 2.204685 10 224 24 8 -12 295 2.350248 11 277 48 * 8 -13 420 2.345397 12 347 48 8 -16 490 2.353941 13 382 96 * 9 -16 669 2.317949 14 613 96 10 -18 900 2.432067 15 693 96 11 -18 980 2.415402 16 771 192 * 11 -19 1346 2.397647 17 865 192 12 -21 1440 2.386947 18 919 384 * 13 -22 2070 2.360695 19 1032 384 14 -23 2183 2.356732 20 1165 384 14 -25 2316 2.356845 21 1252 768 * 15 -25 3555 2.342731 22 1293 768 15 -26 3596 2.317898 23 1373 768 16 -27 3676 2.304183 24 1732 768 17 -29 4035 2.346415 25 2208 768 17 -30 4511 2.392091 26 2314 768 18 -31 4617 2.377687 27 2608 768 18 -33 4911 2.386750 28 2889 768 19 -34 5192 2.391410 29 3221 768 19 -35 5524 2.398793 30 3890 768 20 -36 6193 2.430369 31 4422 768 21 -37 6725 2.444490 32 4419 768 22 -38 6726 2.421901 33 5614 768 22 -39 7917 2.469040 34 6065 768 23 -40 8368 2.470051 35 6837 768 22 -42 9140 2.483612 36 7116 768 23 -42 9419 2.475249 37 8041 768 24 -43 10344 2.490311 38 8356 768 25 -44 10659 2.482618 39 9208 768 26 -45 11511 2.491517 40 10333 768 25 -46 12636 2.505665 41 10799 768 25 -48 13102 2.500883 42 12518 768 26 -49 14821 2.524280 43 13849 768 26 -50 16152 2.535353 44 14190 1536 * 27 -51 18797 2.526378 45 15844 1536 28 -52 20451 2.540426 46 16696 1536 29 -53 21303 2.539523 47 17230 1536 30 -55 21837 2.533515 48 18867 1536 31 -56 23474 2.543182 49 20001 1536 32 -57 24608 2.544706 50 22436 1536 32 -58 27043 2.560931 51 23682 1536 33 -59 28289 2.561780 52 25727 1536 32 -60 30334 2.570152 53 26621 1536 33 -62 31228 2.566425 54 28225 1536 34 -63 32832 2.569066 55 29810 1536 34 -63 34417 2.570937 56 30437 1536 35 -66 35044 2.564599 57 33590 1536 36 -66 38197 2.577752 58 35130 1536 37 -66 39737 2.577751 59 37438 1536 38 -70 42045 2.582549 60 38898 1536 37 -69 43505 2.581292 61 39913 1536 38 -70 44520 2.577179 62 40999 1536 38 -72 45606 2.573530 63 44491 1536 39 -72 49098 2.583320 64 46748 1536 40 -74 51355 2.585436 65 49094 1536 39 -75 53701 2.587563 66 50868 1536 40 -75 55475 2.586607 67 51898 1536 41 -77 56505 2.582123 68 53873 3072 * 41 -78 63088 2.581909 69 57843 3072 42 -79 670S8 2.589800 70 58059 3072 42 -80 67274 2.581906 71 60650 6144 * 43 -81 79081 2.583557 72 62181 6144 44 -82 80612 2.580937 73 64705 6144 45 -84 83136 2.581913 74 68766 6144 46 -85 87197 2.587894 75 72544 6144 46 -86 90975 2.592236 76 79077 6144 47 -87 97508 2.604219 77 80039 6144 48 -88 98470 2.599166 78 81391 6144 47 -90 99822 2.595312 79 82708 6144 48 -91 101139 2.591419 80 86825 6144 49 -92 105256 2.595066 81 90625 6144 50 -92 109056 2.597478 82 95317 6144 49 -94 113748 2.601700 83 98894 6144 50 -95 117325 2.602901 84 102135 6144 50 -96 120566 2.603143 85 105307 6144 51 -97 123738 2.603093 86 108922 6144 51 -98 127353 2.603835 87 113430 6144 52 -100 131861 2.606176 88 116399 6144 53 -101 134830 2.605294 89 119848 6144 54 -101 138279 2.605241 90 126851 6144 55 -103 145282 2.611392 91 130426 12288 * 55 -104 i67289 2.611157 92 136591 12288 55 -105 173454 2.615060 93 139160 12288 56 -106 176023 2.612933 94 141946 12288 56 -107 178809 2.611145 95 150244 12288 57 -108 187107 2.617553 96 154665 12288 58 -110 191528 2.617902 97 157571 12288 58 -112 194434 2.616041 98 160259 12288 58 -111 197122 2.613878 99 162656 12288 59 -112 199519 2.611334 100 168066 12288 59 -114 204929 2.612740 101 169151 12288 60 -115 206014 2.608501 102 174279 12288 61 -116 211142 2.609402 103 176301 12288 62 -117 213164 2.606398 104 179535 12288 63 -118 216398 2.604890 105 183068 12288 63 -120 219931 2.603721 106 185475 12288 63 -120 222338 2.601230 107 191075 12288 64 -123 227938 2.602368 108 193384 12288 64 -122 230247 2.599763 109 198533 24576 * 65 -123 272260 2.600257 110 201592 24576 66 -125 275319 2.598458 111 203638 24576 66 -126 277365 2.595609 112 220540 24576 67 -127 294267 2.607574 113 223887 24576 68 -128 297614 2.605857 114 226905 24576 68 -129 300632 2.603837 115 230614 24576 69 -131 304341 2.602461 116 238570 24576 69 -132 312297 2.604856 117 245731 24576 70 -133 319458 2.606371 118 257250 24576 70 -134 330977 2.611324 119 262693 24576 71 -135 336420 2.611094 120 266949 24576 72 -136 340676 2.609887 121 275964 24576 72 -137 349691 2.612296 122 283742 24576 73 -139 357469 2.613607 123 291458 24576 74 -140 365185 2.614748 124 295630 24576 74 -141 369357 2.613305 125 313456 24576 75 -141 387183 2.621084 126 320362 24576 76 -143 394089 2.621271 127 339479 24576 77 -144 413206 2.628959 128 342052 24576 76 -145 415779 2.626265 129 343547 24576 78 -146 417274 2.622957 130 347760 24576 77 -147 421487 2.621300 131 355873 24576 77 -148 429600 2.621910 ------------------------------------------------- i row index v preperiod length of (g(i,j))_j p period length of (g(i,j))_j an asterisk behind the value indicates, it is distinct from the previous max max { g(i,j)-j | j >= v} min min { g(i,j)-j | j >= v} s highest j-index whose g-value can't be predicted (due to N. Pink) = 3 lcm{p_i} + max{v_i + i} (Prop. 2, Dissertation 1993)