A figurate number made by a cube surmounted by a square pyramid. more
The first 600 house numbers :
1,
9,
32,
78,
155,
271,
434,
652,
933,
1285,
1716,
2234,
2847,
3563,
4390,
5336,
6409,
7617,
8968,
10470,
12131,
13959,
15962,
18148,
20525,
23101,
25884,
28882,
32103,
35555,
39246,
43184,
47377,
51833,
56560,
61566,
66859,
72447,
78338,
84540,
91061,
97909,
105092,
112618,
120495,
128731,
137334,
146312,
155673,
165425,
175576,
186134,
197107,
208503,
220330,
232596,
245309,
258477,
272108,
286210,
300791,
315859,
331422,
347488,
364065,
381161,
398784,
416942,
435643,
454895,
474706,
495084,
516037,
537573,
559700,
582426,
605759,
629707,
654278,
679480,
705321,
731809,
758952,
786758,
815235,
844391,
874234,
904772,
936013,
967965,
1000636,
1034034,
1068167,
1103043,
1138670,
1175056,
1212209,
1250137,
1288848,
1328350,
1368651,
1409759,
1451682,
1494428,
1538005,
1582421,
1627684,
1673802,
1720783,
1768635,
1817366,
1866984,
1917497,
1968913,
2021240,
2074486,
2128659,
2183767,
2239818,
2296820,
2354781,
2413709,
2473612,
2534498,
2596375,
2659251,
2723134,
2788032,
2853953,
2920905,
2988896,
3057934,
3128027,
3199183,
3271410,
3344716,
3419109,
3494597,
3571188,
3648890,
3727711,
3807659,
3888742,
3970968,
4054345,
4138881,
4224584,
4311462,
4399523,
4488775,
4579226,
4670884,
4763757,
4857853,
4953180,
5049746,
5147559,
5246627,
5346958,
5448560,
5551441,
5655609,
5761072,
5867838,
5975915,
6085311,
6196034,
6308092,
6421493,
6536245,
6652356,
6769834,
6888687,
7008923,
7130550,
7253576,
7378009,
7503857,
7631128,
7759830,
7889971,
8021559,
8154602,
8289108,
8425085,
8562541,
8701484,
8841922,
8983863,
9127315,
9272286,
9418784,
9566817,
9716393,
9867520,
10020206,
10174459,
10330287,
10487698,
10646700,
10807301,
10969509,
11133332,
11298778,
11465855,
11634571,
11804934,
11976952,
12150633,
12325985,
12503016,
12681734,
12862147,
13044263,
13228090,
13413636,
13600909,
13789917,
13980668,
14173170,
14367431,
14563459,
14761262,
14960848,
15162225,
15365401,
15570384,
15777182,
15985803,
16196255,
16408546,
16622684,
16838677,
17056533,
17276260,
17497866,
17721359,
17946747,
18174038,
18403240,
18634361,
18867409,
19102392,
19339318,
19578195,
19819031,
20061834,
20306612,
20553373,
20802125,
21052876,
21305634,
21560407,
21817203,
22076030,
22336896,
22599809,
22864777,
23131808,
23400910,
23672091,
23945359,
24220722,
24498188,
24777765,
25059461,
25343284,
25629242,
25917343,
26207595,
26500006,
26794584,
27091337,
27390273,
27691400,
27994726,
28300259,
28608007,
28917978,
29230180,
29544621,
29861309,
30180252,
30501458,
30824935,
31150691,
31478734,
31809072,
32141713,
32476665,
32813936,
33153534,
33495467,
33839743,
34186370,
34535356,
34886709,
35240437,
35596548,
35955050,
36315951,
36679259,
37044982,
37413128,
37783705,
38156721,
38532184,
38910102,
39290483,
39673335,
40058666,
40446484,
40836797,
41229613,
41624940,
42022786,
42423159,
42826067,
43231518,
43639520,
44050081,
44463209,
44878912,
45297198,
45718075,
46141551,
46567634,
46996332,
47427653,
47861605,
48298196,
48737434,
49179327,
49623883,
50071110,
50521016,
50973609,
51428897,
51886888,
52347590,
52811011,
53277159,
53746042,
54217668,
54692045,
55169181,
55649084,
56131762,
56617223,
57105475,
57596526,
58090384,
58587057,
59086553,
59588880,
60094046,
60602059,
61112927,
61626658,
62143260,
62662741,
63185109,
63710372,
64238538,
64769615,
65303611,
65840534,
66380392,
66923193,
67468945,
68017656,
68569334,
69123987,
69681623,
70242250,
70805876,
71372509,
71942157,
72514828,
73090530,
73669271,
74251059,
74835902,
75423808,
76014785,
76608841,
77205984,
77806222,
78409563,
79016015,
79625586,
80238284,
80854117,
81473093,
82095220,
82720506,
83348959,
83980587,
84615398,
85253400,
85894601,
86539009,
87186632,
87837478,
88491555,
89148871,
89809434,
90473252,
91140333,
91810685,
92484316,
93161234,
93841447,
94524963,
95211790,
95901936,
96595409,
97292217,
97992368,
98695870,
99402731,
100112959,
100826562,
101543548,
102263925,
102987701,
103714884,
104445482,
105179503,
105916955,
106657846,
107402184,
108149977,
108901233,
109655960,
110414166,
111175859,
111941047,
112709738,
113481940,
114257661,
115036909,
115819692,
116606018,
117395895,
118189331,
118986334,
119786912,
120591073,
121398825,
122210176,
123025134,
123843707,
124665903,
125491730,
126321196,
127154309,
127991077,
128831508,
129675610,
130523391,
131374859,
132230022,
133088888,
133951465,
134817761,
135687784,
136561542,
137439043,
138320295,
139205306,
140094084,
140986637,
141882973,
142783100,
143687026,
144594759,
145506307,
146421678,
147340880,
148263921,
149190809,
150121552,
151056158,
151994635,
152936991,
153883234,
154833372,
155787413,
156745365,
157707236,
158673034,
159642767,
160616443,
161594070,
162575656,
163561209,
164550737,
165544248,
166541750,
167543251,
168548759,
169558282,
170571828,
171589405,
172611021,
173636684,
174666402,
175700183,
176738035,
177779966,
178825984,
179876097,
180930313,
181988640,
183051086,
184117659,
185188367,
186263218,
187342220,
188425381,
189512709,
190604212,
191699898,
192799775,
193903851,
195012134,
196124632,
197241353,
198362305,
199487496,
200616934,
201750627,
202888583,
204030810,
205177316,
206328109,
207483197,
208642588,
209806290,
210974311,
212146659,
213323342,
214504368,
215689745,
216879481,
218073584,
219272062,
220474923,
221682175,
222893826,
224109884,
225330357,
226555253,
227784580,
229018346,
230256559,
231499227,
232746358,
233997960,
235254041,
236514609,
237779672,
239049238,
240323315,
241601911,
242885034,
244172692,
245464893,
246761645,
248062956,
249368834,
250679287,
251994323,
253313950,
254638176,
255967009,
257300457,
258638528,
259981230,
261328571,
262680559,
264037202,
265398508,
266764485,
268135141,
269510484,
270890522,
272275263,
273664715,
275058886,
276457784,
277861417,
279269793,
280682920,
282100806,
283523459,
284950887,
286383098,
287820100.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 90856 values, from 1 to 999994893864796).
n\r | 0 | 1 |
2 | 45428 | 45428 | 2 |
3 | 30285 | 30286 | 30285 | 3 |
4 | 22714 | 22714 | 22714 | 22714 | 4 |
5 | 18171 | 18172 | 18171 | 18171 | 18171 | 5 |
6 | 15142 | 15143 | 15143 | 15143 | 15143 | 15142 | 6 |
7 | 12979 | 38938 | 12980 | 0 | 12980 | 12979 | 0 | 7 |
8 | 11357 | 11358 | 11357 | 11357 | 11357 | 11356 | 11357 | 11357 | 8 |
9 | 10095 | 10096 | 10095 | 10095 | 10095 | 10095 | 10095 | 10095 | 10095 | 9 |
10 | 9085 | 9086 | 9086 | 9086 | 9086 | 9086 | 9086 | 9085 | 9085 | 9085 | 10 |
11 | 8259 | 24780 | 0 | 8259 | 0 | 8260 | 0 | 8260 | 0 | 24778 | 8260 |
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.