### Who's Online

We have 41 guests and no members online

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 ...