Article Index

Carréphylic classes: n2-n/2 (for even n)

Here are the first 6 carréphylic numbers of the form n2-n/2 (for even n) with the usual data.
Root-3 is a 'small numbers exception' on the general pattern because it is also a member of n2-1 and shows the characteristic 'sp-block shift' of that class.
The first non-trivial ab-blocks (second for root-3) follow a simple pattern (4n-1)/4. The s/p- and t/q-fractions are the only ones above the root-value.
The values 'v' equal half the numerator of the first t/q fraction and the numerator of the first q/t fraction respectively.

√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 ...

√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 ...

√33
 1 0 1 2 3 4 5 6 11 17 23 132 155 178 201 224 247 270 517 787 1057 6072 7129 8186 9243 10300 11357 12414 23771 36185 48599 279180 327779 376378 424977 473576 522175 570774 1092949 1663723 2234497 12836208 15070705 17305202 19539699 21774196 24008693 26243190 50251883 76495073 102738263 590186388 ... 0 1 1 1 1 1 1 1 2 3 4 23 27 31 35 39 43 47 90 137 184 1057 1241 1425 1609 1793 1977 2161 4138 6299 8460 48599 57059 65519 73979 82439 90899 99359 190258 289617 388976 2234497 2623473 3012449 3401425 3790401 4179377 4568353 8747730 13316083 17884436 102738263 ...

√60
 1 0 1 2 3 4 5 6 7 8 15 23 31 240 271 302 333 364 395 426 457 488 945 1433 1921 14880 16801 18722 20643 22564 24485 26406 28327 30248 58575 88823 119071 922320 1041391 1160462 1279533 1398604 1517675 1636746 1755817 1874888 3630705 5505593 7380481 57168960 64549441 71929922 79310403 86690884 94071365 101451846 108832327 116212808 225045135 341257943 457470751 3543553200 ... 0 1 1 1 1 1 1 1 1 1 2 3 4 31 35 39 43 47 51 55 59 63 122 185 248 1921 2169 2417 2665 2913 3161 3409 3657 3905 7562 11467 15372 119071 134443 149815 165187 180559 195931 211303 226675 242047 468659 710769 952816 7380481 8333297 9286113 10238929 11191745 12144561 13097377 14050193 15003009 29045391 44056211 59059220 457470751 ...

√95
 1 0 1 2 3 4 5 6 7 8 9 10 19 29 39 380 419 458 497 536 575 614 653 692 731 770 1501 2271 3041 29640 ... 0 1 1 1 1 1 1 1 1 1 1 1 2 3 4 39 43 47 51 55 59 63 67 71 75 79 154 233 312 3041 ...

√138
 1 0 1 2 3 4 5 6 7 8 9 10 11 12 23 35 47 552 599 646 693 740 787 834 881 928 975 1022 1069 1116 2185 3301 4417 51888 ... 0 1 1 1 1 1 1 1 1 1 1 1 1 1 2 3 4 47 51 55 59 63 67 71 75 79 83 87 91 95 186 281 376 4417 ...