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Carréphylic classes: n2-2
Here are the first 10 carréphylic numbers of the form n2-2 with the usual data.
Note that all fractions except the s/p- and t/q-fractions are below the root-value.
A nice tq-pattern over even and odd squares.
For all t/q fractions involved: | v = 2 | |||
For q/t-fractions 'q' follows: | U(1,7,4)2 | 1, 7, 17, 31, 49, 71, ... | ||
while 'v' follows its negative: | U(-1,-7,-4)2 | -1, -7, -17, -31, -49, -71, ... |
√7
1 | 0 | 1 | 2 | 3 | 5 | 8 | 21 | 29 | 37 | 45 | 82 | 127 | 336 | 463 | 590 | 717 | 1307 | 2024 | 5355 | 7379 | 9403 | 11427 | 20830 | 32257 | 85344 | 117601 | 149858 | 182115 | 331973 | 514088 | 1360149 | 1874237 | 2388325 | 2902413 | 5290738 | 8193151 | 21677040 | 29870191 | 38063342 | 46256493 | 84319835 | 130576328 | 345472491 | ... |
0 | 1 | 1 | 1 | 1 | 2 | 3 | 8 | 11 | 14 | 17 | 31 | 48 | 127 | 175 | 223 | 271 | 494 | 765 | 2024 | 2789 | 3554 | 4319 | 7873 | 12192 | 32257 | 44449 | 56641 | 68833 | 125474 | 194307 | 514088 | 708395 | 902702 | 1097009 | 1999711 | 3096720 | 8193151 | 11289871 | 14386591 | 17483311 | 31869902 | 49353213 | 130576328 | ... |
√14
1 | 0 | 1 | 2 | 3 | 4 | 7 | 11 | 15 | 56 | 71 | 86 | 101 | 116 | 217 | 333 | 449 | 1680 | 2129 | 2578 | 3027 | 3476 | 6503 | 9979 | 13455 | 50344 | 63799 | 77254 | 90709 | 104164 | 194873 | 299037 | 403201 | 1508640 | 1911841 | 2315042 | 2718243 | 3121444 | 5839687 | 8961131 | 12082575 | 45208856 | ... |
0 | 1 | 1 | 1 | 1 | 1 | 2 | 3 | 4 | 15 | 19 | 23 | 27 | 31 | 58 | 89 | 120 | 449 | 569 | 689 | 809 | 929 | 1738 | 2667 | 3596 | 13455 | 17051 | 20647 | 24243 | 27839 | 52082 | 79921 | 107760 | 403201 | 510961 | 618721 | 726481 | 834241 | 1560722 | 2394963 | 3229204 | 12082575 | ... |
√23
1 | 0 | 1 | 2 | 3 | 4 | 5 | 14 | 19 | 24 | 115 | 139 | 163 | 187 | 211 | 235 | 681 | 916 | 1151 | 5520 | 6671 | 7822 | 8973 | 10124 | 11275 | 32674 | 43949 | 55224 | 264845 | 320069 | 375293 | 430517 | 485741 | 540965 | 1567671 | 2108636 | 2649601 | 12707040 | 15356641 | 18006242 | 20655843 | 23305444 | 25955045 | 75215534 | 101170579 | 127125624 | 609673075 | ... |
0 | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 4 | 5 | 24 | 29 | 34 | 39 | 44 | 49 | 142 | 191 | 240 | 1151 | 1391 | 1631 | 1871 | 2111 | 2351 | 6813 | 9164 | 11515 | 55224 | 66739 | 375293 | 89769 | 101284 | 112799 | 326882 | 439681 | 552480 | 2649601 | 3202081 | 3754561 | 4307041 | 4859521 | 5412001 | 15683523 | 21095524 | 26507525 | 127125624 | ... |
√34
1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 17 | 23 | 29 | 35 | 204 | 239 | 274 | 309 | 344 | 379 | 414 | 1207 | 1621 | 2035 | 2449 | 14280 | 16729 | 19178 | 21627 | 24076 | 26525 | 28974 | 84473 | 113447 | 142421 | 171395 | 999396 | 1170791 | 1342186 | 1513581 | 1684976 | 1856371 | 2027766 | 5911903 | 7939669 | 9967435 | 11995201 | 69943440 | ... |
0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 4 | 5 | 6 | 35 | 41 | 47 | 53 | 59 | 65 | 71 | 207 | 278 | 349 | 420 | 2449 | 2869 | 3289 | 3709 | 4129 | 4549 | 4969 | 14487 | 19456 | 24425 | 29394 | 171395 | 200789 | 230183 | 259577 | 288971 | 318365 | 347759 | 1013883 | 1361642 | 1709401 | 2057160 | 11995201 | ... |
√47
1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 27 | 34 | 41 | 48 | 329 | 377 | 425 | 473 | 521 | 569 | 617 | 665 | 2612 | 3277 | 3942 | 4607 | 31584 | 36191 | 40798 | 45405 | 50012 | 54619 | 59226 | 63833 | 250725 | 314558 | 378391 | 442224 | 3031735 | 3473959 | 3916183 | 4358407 | 4800631 | 5242855 | 5685079 | 6127303 | 24066988 | 30194291 | 36321594 | 42448897 | 291014976 | ... |
0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 4 | 5 | 6 | 7 | 48 | 55 | 62 | 69 | 76 | 83 | 90 | 97 | 381 | 478 | 575 | 672 | 4607 | 5279 | 5951 | 6623 | 7295 | 7967 | 8639 | 9311 | 36572 | 45883 | 55194 | 64505 | 442224 | 506729 | 571234 | 635739 | 700244 | 764749 | 829254 | 893759 | 3510531 | 4404290 | 5298049 | 6191808 | 42448897 | ... |
√62
1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 31 | 39 | 47 | 55 | 63 | 496 | 559 | 622 | 685 | 748 | 811 | 874 | 937 | 1000 | 3937 | 4937 | 5937 | 6937 | 7937 | 62496 | 70433 | 78370 | 86307 | 94244 | 102181 | 110118 | 118055 | 125992 | 490631 | 622023 | 748015 | 874007 | 999999 | 7874000 | ... |
0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 4 | 5 | 6 | 7 | 8 | 63 | 71 | 79 | 87 | 95 | 103 | 111 | 119 | 127 | 500 | 627 | 754 | 881 | 1008 | 7937 | 8945 | 9953 | 10961 | 11969 | 12977 | 13985 | 14993 | 16001 | 62996 | 78997 | 94998 | 110999 | 127000 | 999999 | ... |
√79
1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 44 | 53 | 62 | 71 | 80 | 711 | 791 | 871 | 951 | 1031 | 1111 | 1191 | 1271 | 1351 | 1431 | 7075 | 8506 | 9937 | 11368 | 12799 | 113760 | ... |
0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 5 | 6 | 7 | 8 | 9 | 80 | 89 | 98 | 107 | 116 | 125 | 134 | 143 | 152 | 161 | 796 | 957 | 1118 | 1279 | 1440 | 12799 | ... |
√98
1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 49 | 59 | 69 | 79 | 89 | 99 | 980 | 1079 | 1178 | 1277 | 1376 | 1475 | 1574 | 1673 | 1772 | 1871 | 1970 | 9751 | 11721 | 13691 | 15661 | 17631 | 19601 | 194040 | ... |
0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 5 | 6 | 7 | 8 | 9 | 10 | 99 | 109 | 119 | 129 | 139 | 149 | 159 | 169 | 179 | 189 | 199 | 985 | 1184 | 1383 | 1582 | 1781 | 1980 | 19601 | ... |
√119
1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 65 | 76 | 87 | 98 | 109 | 120 | 1309 | 1429 | 1549 | 1669 | 1789 | 1909 | 2029 | 2149 | 2269 | 2389 | 2509 | 2629 | 15654 | 18283 | 20912 | 23541 | 26170 | 28799 | 314160 | ... |
0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 6 | 7 | 8 | 9 | 10 | 11 | 120 | 131 | 142 | 153 | 164 | 175 | 186 | 197 | 208 | 219 | 230 | 241 | 1435 | 1676 | 1917 | 2158 | 2399 | 2640 | 28799 | ... |
√142
1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 71 | 83 | 95 | 107 | 119 | 131 | 143 | 1704 | 1847 | 1990 | 2133 | 2276 | 2419 | 2562 | 2705 | 2848 | 2991 | 3134 | 3277 | 3420 | 20377 | 23797 | 27217 | 30637 | 34057 | 37477 | 40897 | 487344 | ... |
0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 143 | 155 | 167 | 179 | 191 | 203 | 215 | 227 | 239 | 251 | 263 | 275 | 287 | 1710 | 1997 | 2284 | 2571 | 2858 | 3145 | 3432 | 40897 | ... |