Saturday, May 30, 2015

Triangular Numbers, Tetrahedral Numbers, and the NERDY Numbers that Produce Them

5/30/2015

 Triangular Numbers: The decimal expansion of the inverse of 999,700,029,999 produces a sequence showing the triangular numbers. 1/99970002999 = 0. 0000 0000 0001 0003 0006 0010 0015 0021 0028 0036 0045 0055 0066 0078 0091 0105 0120 0136 0153 0171 0190 0210 0231 0253 0276 0300 0325 0351 0378 0406 0435 0465 0496 0528 0561 0595 0630 0666 0703 0741 0780 0820 0861 0903 0946 0990 1035 1081 1128 1176 1225 1275 1326 1378 1431 1485 1540 1596 1653 1711 1770 1830 1891 1953 2016 2080 2145 2211 2278 2346 2415 2485 2556 2628 2701 … Tetrahedral Numbers The decimal expansion of the inverse of 9,996,000,599,960,001 produces a sequence showing the tetrahedral numbers. 1/9996000599960001 = 0. 0000 0000 0001 0004 0010 0020 0035 0056 0084 0120 0165 0220 0286 0364 0455 0560 0680 0816 0969 1140 1330 1540 1771 2024 2300 2600 2925 3276 3654 4060 4495 4960 5456 5984 6545 7140 7770 8436 9139 …

David

1 comment:

1. 1/999700029999 =

0 . 0000 0000 0001 0003 0006 0010 0015 0021 0028 0036 0045 0055 0066 0078 0091 0105 0120 0136 0153 0171 0190 0210 0231 0253 0276 0300 0325 0351 0378 0406 0435 0465 0496 0528 0561 0595 0630 0666 0703 0741 0780 0820 0861 0903 0946 0990 1035 1081 1128 1176 1225 1275 1326 1378 1431 1485 1540 1596 1653 1711 1770 1830 1891 1953 2016 2080 2145 2211 2278 2346 2415 2485 2556 2628 2701 2775 2850 2926 3003 3081 3160 3240 3321 3403 3486 3570 3655 3741 3828 3916 4005 4095 4186 4278 4371 4465 4560 4656 4753 4851 4950 5050 5151 5253 5356 5460 5565 5671 5778 5886 5995 6105 6216 6328 6441 6555 6670 6786 6903 7021 7140 7260 7381 7503 7626 7750 7875 8001 8128 8256 8385 8515 8646 8778 8911 9045 9180 9316 9453 9591 9730 ...