A figurate number of the form n(n+1)(n+2)/6. more
The first 600 tetrahedral numbers :
1,
4,
10,
20,
35,
56,
84,
120,
165,
220,
286,
364,
455,
560,
680,
816,
969,
1140,
1330,
1540,
1771,
2024,
2300,
2600,
2925,
3276,
3654,
4060,
4495,
4960,
5456,
5984,
6545,
7140,
7770,
8436,
9139,
9880,
10660,
11480,
12341,
13244,
14190,
15180,
16215,
17296,
18424,
19600,
20825,
22100,
23426,
24804,
26235,
27720,
29260,
30856,
32509,
34220,
35990,
37820,
39711,
41664,
43680,
45760,
47905,
50116,
52394,
54740,
57155,
59640,
62196,
64824,
67525,
70300,
73150,
76076,
79079,
82160,
85320,
88560,
91881,
95284,
98770,
102340,
105995,
109736,
113564,
117480,
121485,
125580,
129766,
134044,
138415,
142880,
147440,
152096,
156849,
161700,
166650,
171700,
176851,
182104,
187460,
192920,
198485,
204156,
209934,
215820,
221815,
227920,
234136,
240464,
246905,
253460,
260130,
266916,
273819,
280840,
287980,
295240,
302621,
310124,
317750,
325500,
333375,
341376,
349504,
357760,
366145,
374660,
383306,
392084,
400995,
410040,
419220,
428536,
437989,
447580,
457310,
467180,
477191,
487344,
497640,
508080,
518665,
529396,
540274,
551300,
562475,
573800,
585276,
596904,
608685,
620620,
632710,
644956,
657359,
669920,
682640,
695520,
708561,
721764,
735130,
748660,
762355,
776216,
790244,
804440,
818805,
833340,
848046,
862924,
877975,
893200,
908600,
924176,
939929,
955860,
971970,
988260,
1004731,
1021384,
1038220,
1055240,
1072445,
1089836,
1107414,
1125180,
1143135,
1161280,
1179616,
1198144,
1216865,
1235780,
1254890,
1274196,
1293699,
1313400,
1333300,
1353400,
1373701,
1394204,
1414910,
1435820,
1456935,
1478256,
1499784,
1521520,
1543465,
1565620,
1587986,
1610564,
1633355,
1656360,
1679580,
1703016,
1726669,
1750540,
1774630,
1798940,
1823471,
1848224,
1873200,
1898400,
1923825,
1949476,
1975354,
2001460,
2027795,
2054360,
2081156,
2108184,
2135445,
2162940,
2190670,
2218636,
2246839,
2275280,
2303960,
2332880,
2362041,
2391444,
2421090,
2450980,
2481115,
2511496,
2542124,
2573000,
2604125,
2635500,
2667126,
2699004,
2731135,
2763520,
2796160,
2829056,
2862209,
2895620,
2929290,
2963220,
2997411,
3031864,
3066580,
3101560,
3136805,
3172316,
3208094,
3244140,
3280455,
3317040,
3353896,
3391024,
3428425,
3466100,
3504050,
3542276,
3580779,
3619560,
3658620,
3697960,
3737581,
3777484,
3817670,
3858140,
3898895,
3939936,
3981264,
4022880,
4064785,
4106980,
4149466,
4192244,
4235315,
4278680,
4322340,
4366296,
4410549,
4455100,
4499950,
4545100,
4590551,
4636304,
4682360,
4728720,
4775385,
4822356,
4869634,
4917220,
4965115,
5013320,
5061836,
5110664,
5159805,
5209260,
5259030,
5309116,
5359519,
5410240,
5461280,
5512640,
5564321,
5616324,
5668650,
5721300,
5774275,
5827576,
5881204,
5935160,
5989445,
6044060,
6099006,
6154284,
6209895,
6265840,
6322120,
6378736,
6435689,
6492980,
6550610,
6608580,
6666891,
6725544,
6784540,
6843880,
6903565,
6963596,
7023974,
7084700,
7145775,
7207200,
7268976,
7331104,
7393585,
7456420,
7519610,
7583156,
7647059,
7711320,
7775940,
7840920,
7906261,
7971964,
8038030,
8104460,
8171255,
8238416,
8305944,
8373840,
8442105,
8510740,
8579746,
8649124,
8718875,
8789000,
8859500,
8930376,
9001629,
9073260,
9145270,
9217660,
9290431,
9363584,
9437120,
9511040,
9585345,
9660036,
9735114,
9810580,
9886435,
9962680,
10039316,
10116344,
10193765,
10271580,
10349790,
10428396,
10507399,
10586800,
10666600,
10746800,
10827401,
10908404,
10989810,
11071620,
11153835,
11236456,
11319484,
11402920,
11486765,
11571020,
11655686,
11740764,
11826255,
11912160,
11998480,
12085216,
12172369,
12259940,
12347930,
12436340,
12525171,
12614424,
12704100,
12794200,
12884725,
12975676,
13067054,
13158860,
13251095,
13343760,
13436856,
13530384,
13624345,
13718740,
13813570,
13908836,
14004539,
14100680,
14197260,
14294280,
14391741,
14489644,
14587990,
14686780,
14786015,
14885696,
14985824,
15086400,
15187425,
15288900,
15390826,
15493204,
15596035,
15699320,
15803060,
15907256,
16011909,
16117020,
16222590,
16328620,
16435111,
16542064,
16649480,
16757360,
16865705,
16974516,
17083794,
17193540,
17303755,
17414440,
17525596,
17637224,
17749325,
17861900,
17974950,
18088476,
18202479,
18316960,
18431920,
18547360,
18663281,
18779684,
18896570,
19013940,
19131795,
19250136,
19368964,
19488280,
19608085,
19728380,
19849166,
19970444,
20092215,
20214480,
20337240,
20460496,
20584249,
20708500,
20833250,
20958500,
21084251,
21210504,
21337260,
21464520,
21592285,
21720556,
21849334,
21978620,
22108415,
22238720,
22369536,
22500864,
22632705,
22765060,
22897930,
23031316,
23165219,
23299640,
23434580,
23570040,
23706021,
23842524,
23979550,
24117100,
24255175,
24393776,
24532904,
24672560,
24812745,
24953460,
25094706,
25236484,
25378795,
25521640,
25665020,
25808936,
25953389,
26098380,
26243910,
26389980,
26536591,
26683744,
26831440,
26979680,
27128465,
27277796,
27427674,
27578100,
27729075,
27880600,
28032676,
28185304,
28338485,
28492220,
28646510,
28801356,
28956759,
29112720,
29269240,
29426320,
29583961,
29742164,
29900930,
30060260,
30220155,
30380616,
30541644,
30703240,
30865405,
31028140,
31191446,
31355324,
31519775,
31684800,
31850400,
32016576,
32183329,
32350660,
32518570,
32687060,
32856131,
33025784,
33196020,
33366840,
33538245,
33710236,
33882814,
34055980,
34229735,
34404080,
34579016,
34754544,
34930665,
35107380,
35284690,
35462596,
35641099,
35820200,
35999900,
36180200.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 181711 values, from 1 to 999999021225736).
n\r | 0 | 1 |
2 | 136283 | 45428 | 2 |
3 | 60570 | 60571 | 60570 | 3 |
4 | 113569 | 22714 | 22714 | 22714 | 4 |
5 | 109026 | 36343 | 0 | 0 | 36342 | 5 |
6 | 45427 | 15142 | 45427 | 15143 | 45429 | 15143 | 6 |
7 | 77875 | 25959 | 0 | 25959 | 25959 | 0 | 25959 | 7 |
8 | 56784 | 11357 | 11357 | 11357 | 56785 | 11357 | 11357 | 11357 | 8 |
9 | 20190 | 20191 | 20190 | 20190 | 20190 | 20190 | 20190 | 20190 | 20190 | 9 |
10 | 81769 | 9086 | 0 | 0 | 27257 | 27257 | 27257 | 0 | 0 | 9085 | 10 |
11 | 49557 | 33039 | 16519 | 0 | 16520 | 0 | 0 | 16519 | 0 | 16519 | 33038 |
A pictorial representation of the table above
Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.