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Carréphylic classes: n2-1
Here are the first 10 carréphylic numbers of the form n2-1 with the usual data.
For numbers 'n' that are one less than a square, or N2-n = 1, the formula gives the sp-fraction and factor of the base-2 accelleration of the series.
The first fraction is N/1, F=2N, because obviously N2-n*12 = 1 is a solution of the diophantine equation.
Note that the q/t fractions immediately precede the sp-blocks, that their v-value decreases with steps of 2 over 'n' and that all approximations except the s/p-fractions are below the root-value.
Compare n2+n.
√3
| 1 | 0 | 1 | 2 | 3 | 5 | 7 | 12 | 19 | 26 | 45 | 71 | 97 | 168 | 265 | 362 | 627 | 989 | 1351 | 2340 | 3691 | 5042 | 8733 | 13775 | 18817 | 32592 | 51409 | 70226 | 121635 | 191861 | 262087 | 453948 | 716035 | 978122 | 1694157 | ... |
| 0 | 1 | 1 | 1 | 2 | 3 | 4 | 7 | 11 | 15 | 26 | 41 | 56 | 97 | 153 | 209 | 362 | 571 | 780 | 1351 | 2131 | 2911 | 5042 | 7953 | 10864 | 18817 | 29681 | 40545 | 70226 | 110771 | 151316 | 262087 | 413403 | 564719 | 978122 | ... |
√8
| 1 | 0 | 1 | 2 | 3 | 8 | 11 | 14 | 17 | 48 | 65 | 82 | 99 | 280 | 379 | 478 | 577 | 1632 | 2209 | 2786 | 3363 | 9512 | 12875 | 16238 | 19601 | 55440 | 75041 | 94642 | 114243 | 323128 | 437371 | 551614 | 665857 | 1883328 | 2549185 | 3215042 | 3880899 | 10976840 | 14857739 | 18738638 | 22619537 | 63977712 | ... |
| 0 | 1 | 1 | 1 | 1 | 3 | 4 | 5 | 6 | 17 | 23 | 29 | 35 | 99 | 134 | 169 | 204 | 577 | 781 | 985 | 1189 | 3363 | 4552 | 5741 | 6930 | 19601 | 26531 | 33461 | 40391 | 114243 | 154634 | 195025 | 235416 | 665857 | 901273 | 1136689 | 1372105 | 3880899 | 5253004 | 6625109 | 7997214 | 22619537 | ... |
√15
| 1 | 0 | 1 | 2 | 3 | 4 | 15 | 19 | 23 | 27 | 31 | 120 | 151 | 182 | 213 | 244 | 945 | 1189 | 1433 | 1677 | 1921 | 7440 | 9361 | 11282 | 13203 | 15124 | 58575 | 73699 | 88823 | 103947 | 119071 | 461160 | 580231 | 699302 | 818373 | 937444 | 3630705 | 4568149 | 5505593 | 6443037 | 7380481 | 28584480 | ... |
| 0 | 1 | 1 | 1 | 1 | 1 | 4 | 5 | 6 | 7 | 8 | 31 | 39 | 47 | 55 | 63 | 244 | 307 | 370 | 433 | 496 | 1921 | 2417 | 2913 | 3409 | 3905 | 15124 | 19029 | 22934 | 26839 | 30744 | 119071 | 149815 | 180559 | 211303 | 242047 | 937444 | 1179491 | 1421538 | 1663585 | 1905632 | 7380481 | ... |
√24
| 1 | 0 | 1 | 2 | 3 | 4 | 5 | 24 | 29 | 34 | 39 | 44 | 49 | 240 | 289 | 338 | 387 | 436 | 485 | 2376 | 2861 | 3346 | 3831 | 4316 | 4801 | 23520 | 28321 | 33122 | 37923 | 42724 | 47525 | 232824 | 280349 | 327874 | 375399 | 422924 | 470449 | 2304720 | 2775169 | 3245618 | 3716067 | 4186516 | 4656965 | 22814376 | 27471341 | 32128306 | 36785271 | 41442236 | 46099201 | 225839040 | ... |
| 0 | 1 | 1 | 1 | 1 | 1 | 1 | 5 | 6 | 7 | 8 | 9 | 10 | 49 | 59 | 69 | 79 | 89 | 99 | 485 | 584 | 683 | 782 | 881 | 980 | 4801 | 5781 | 6761 | 7741 | 8721 | 9701 | 47525 | 57226 | 66927 | 76628 | 86329 | 96030 | 470449 | 566479 | 662509 | 758539 | 854569 | 950599 | 4656965 | 5607564 | 6558163 | 7508762 | 8459361 | 9409960 | 46099201 | ... |
√35
| 1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 35 | 41 | 47 | 53 | 59 | 65 | 71 | 420 | 491 | 562 | 633 | 704 | 775 | 846 | 5005 | 5851 | 6697 | 7543 | 8389 | 9235 | 10081 | 59640 | 69721 | 79802 | 89883 | 99964 | 110045 | 120126 | 710675 | 830801 | 950927 | 1071053 | 1191179 | 1311305 | 1431431 | 8468460 | 9899891 | 11331322 | 12762753 | 14194184 | 15625615 | 17057046 | 100910845 | ... |
| 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 71 | 83 | 95 | 107 | 119 | 131 | 143 | 846 | 989 | 1132 | 1275 | 1418 | 1561 | 1704 | 10081 | 11785 | 13489 | 15193 | 16897 | 18601 | 20305 | 120126 | 140431 | 160736 | 181041 | 201346 | 221651 | 241956 | 1431431 | 1673387 | 1915343 | 2157299 | 2399255 | 2641211 | 2883167 | 17057046 | ... |
√48
| 1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 48 | 55 | 62 | 69 | 76 | 83 | 90 | 97 | 672 | 769 | 866 | 963 | 1060 | 1157 | 1254 | 1351 | 9360 | 10711 | 12062 | 13413 | 14764 | 16115 | 17466 | 18817 | 130368 | 149185 | 168002 | 186819 | 205636 | 224453 | 243270 | 262087 | 1815792 | 2077879 | 2339966 | 2602053 | 2864140 | 3126227 | 3388314 | 3650401 | 25290720 | ... |
| 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 97 | 111 | 125 | 139 | 153 | 167 | 181 | 195 | 1351 | 1546 | 1741 | 1936 | 2131 | 2326 | 2521 | 2716 | 18817 | 21533 | 24249 | 26965 | 29681 | 32397 | 35113 | 37829 | 262087 | 299916 | 337745 | 375574 | 413403 | 451232 | 489061 | 526890 | 3650401 | ... |
√63
| 1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 63 | 71 | 79 | 87 | 95 | 103 | 111 | 119 | 127 | 1008 | 1135 | 1262 | 1389 | 1516 | 1643 | 1770 | 1897 | 2024 | 16065 | 18089 | 20113 | 22137 | 24161 | 26185 | 28209 | 30233 | 32257 | 256032 | ... |
| 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 127 | 143 | 159 | 175 | 191 | 207 | 223 | 239 | 255 | 2024 | 2279 | 2534 | 2789 | 3044 | 3299 | 3554 | 3809 | 4064 | 32257 | ... |
√80
| 1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 80 | 89 | 98 | 107 | 116 | 125 | 134 | 143 | 152 | 161 | 1440 | 1601 | 1762 | 1923 | 2084 | 2245 | 2406 | 2567 | 2728 | 2889 | 25840 | 28729 | 31618 | 34507 | 37396 | 40285 | 43174 | 46063 | 48952 | 51841 | 463680 | 515521 | 567362 | 619203 | 671044 | 722885 | 774726 | 826567 | 878408 | 930249 | 8320400 | 9250649 | 10180898 | 11111147 | 12041396 | 12971645 | 13901894 | 14832143 | 15762392 | 16692641 | 149303520 | 165996161 | 182688802 | 199381443 | 216074084 | 232766725 | 249459366 | 266152007 | 282844648 | 299537289 | 2679142960 | ... |
| 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 161 | 179 | 197 | 215 | 233 | 251 | 269 | 287 | 305 | 323 | 2889 | 3212 | 3535 | 3858 | 4181 | 4504 | 4827 | 5150 | 5473 | 5796 | 51841 | 57637 | 63433 | 69229 | 75025 | 80821 | 86617 | 92413 | 98209 | 104005 | 930249 | 1034254 | 1138259 | 1242264 | 1346269 | 1450274 | 1554279 | 1658284 | 1762289 | 1866294 | 16692641 | 18558935 | 20425229 | 22291523 | 24157817 | 26024111 | 27890405 | 29756699 | 31622993 | 33489287 | 299537289 | ... |
√99
| 1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 99 | 109 | 119 | 129 | 139 | 149 | 159 | 169 | 179 | 189 | 199 | 1980 | 2179 | 2378 | 2577 | 2776 | 2975 | 3174 | 3373 | 3572 | 3771 | 3970 | 39501 | ... |
| 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 199 | 219 | 239 | 259 | 279 | 299 | 319 | 339 | 359 | 379 | 399 | 3970 | ... |
√120
| 1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 120 | 131 | 142 | 153 | 164 | 175 | 186 | 197 | 208 | 219 | 230 | 241 | 2640 | ... |
| 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 241 | ... |