A number n which can be split into two numbers which seed a Fibonacci-like sequence containing n itself. more
The first 600 fibodiv numbers :
14,
19,
28,
47,
61,
75,
122,
149,
183,
199,
244,
298,
305,
323,
366,
427,
488,
497,
549,
646,
795,
911,
969,
1292,
1301,
1499,
1822,
1999,
2087,
2602,
2733,
2998,
3089,
3248,
3379,
3644,
3903,
4555,
4997,
5204,
5466,
6178,
6377,
6496,
6505,
7288,
7806,
7995,
8199,
8845,
9107,
9161,
9267,
9744,
10408,
11709,
12356,
12992,
13010,
14311,
14999,
15445,
15612,
16913,
17690,
18214,
18322,
18534,
19515,
19999,
20816,
20987,
21623,
22117,
23418,
24712,
24719,
26020,
27321,
27483,
27801,
28622,
29107,
29923,
29998,
30890,
31224,
32498,
32525,
33826,
33979,
35127,
36428,
36644,
37729,
39030,
40331,
41632,
42933,
44234,
45535,
45805,
46836,
48137,
49438,
49997,
50739,
52040,
53341,
54642,
54966,
55943,
57244,
58214,
58545,
59846,
61147,
62448,
63749,
64996,
65050,
66351,
67652,
68953,
70254,
71555,
72856,
74157,
75458,
76759,
78060,
79361,
79995,
80662,
81963,
83264,
84565,
85866,
87089,
87167,
87321,
88468,
88945,
89769,
91070,
91661,
92371,
93672,
94973,
96274,
97494,
97575,
98876,
100177,
101478,
102779,
104080,
105381,
106682,
107983,
109284,
110585,
111886,
113187,
114285,
114488,
115789,
116428,
117090,
118391,
119692,
120993,
122294,
123595,
124896,
126197,
127498,
128799,
129992,
130901,
143911,
145535,
149999,
174178,
174642,
183322,
199999,
203749,
209987,
228570,
232856,
261267,
261802,
261963,
274983,
291232,
299998,
309089,
324998,
339979,
342855,
348356,
366644,
376767,
392703,
435445,
457140,
458305,
493195,
499997,
522534,
523604,
549966,
571425,
582464,
609623,
618178,
649996,
654505,
685710,
696712,
783801,
785406,
799995,
870890,
873696,
889945,
916307,
916661,
927267,
957979,
974994,
986390,
1047208,
1164928,
1178109,
1236356,
1299992,
1309010,
1439911,
1456160,
1479585,
1499999,
1545445,
1596013,
1747392,
1833322,
1854534,
1972780,
1999999,
2038624,
2099987,
2163623,
2329856,
2465975,
2472712,
2749983,
2781801,
2912482,
2999998,
3090890,
3192026,
3249998,
3399979,
3666644,
3769767,
4583305,
4788039,
4934695,
4999997,
5499966,
5824964,
6099623,
6384052,
6499996,
7980065,
7999995,
8612801,
8737446,
8899945,
9166661,
9502214,
9576078,
9749994,
9869390,
10451854,
11172091,
11649928,
12768104,
12999992,
13090901,
14364117,
14399911,
14562410,
14999999,
15960130,
15969013,
17225602,
17474892,
17556143,
18333322,
19004428,
19152156,
19999999,
20387374,
20748169,
20903708,
20999987,
21890647,
22344182,
23299856,
23940195,
25536208,
25838403,
26181802,
27132221,
27499983,
28506642,
28728234,
29124982,
29999998,
30324247,
30909089,
31355562,
31920260,
32499998,
33516273,
33999979,
35112286,
36666644,
36708299,
37699767,
38008856,
38304312,
39272703,
39900325,
41496338,
41807416,
43092351,
43781294,
44688364,
45833305,
46284377,
47511070,
47880390,
49349695,
49476403,
49999997,
51072416,
52259270,
52363604,
52668429,
54264442,
54999966,
55860455,
57013284,
57456468,
58249964,
59052481,
60648494,
60999623,
61818178,
62244507,
63840520,
64999996,
65436533,
65454505,
65671941,
66515498,
67032546,
67645819,
68628559,
70224572,
71820585,
73416598,
75012611,
76017712,
76608624,
78204637,
78545406,
79800650,
79999995,
80212761,
81396663,
82992676,
84588689,
85519926,
86132801,
86184702,
87374946,
87562588,
87780715,
88999945,
89376728,
90972741,
91636307,
91666661,
92568754,
92727267,
94164767,
95022140,
95760780,
97356793,
97499994,
98699390,
98952806,
100548819,
102144832,
103740845,
104524354,
104727208,
105336858,
106932871,
108528884,
109453235,
110124897,
111720910,
113316923,
114026568,
114912936,
116499928,
116508949,
117818109,
118104962,
119700975,
121296988,
123047543,
123528782,
123636356,
126506361,
129999992,
130909010,
131343882,
133030996,
142533210,
143999911,
145624910,
149999999,
152035424,
153234529,
154545445,
159699013,
160425522,
161537638,
171039852,
172265602,
174749892,
175125176,
180542066,
183333322,
185454534,
190044280,
197015823,
199546494,
199999999,
203874874,
209048708,
209999987,
216363623,
218550922,
218906470,
218918647,
228053136,
232999856,
237555350,
240638283,
240797117,
246095086,
247057564,
247272712,
253012722,
256559778,
258398403,
262687764,
266061992,
274999983,
275564206,
278181801,
284578411,
285066420,
291249982,
294568634,
299999998,
304070848,
306469058,
309090890,
313573062,
320851044,
323075276,
324999998,
328359705,
332577490,
339999979,
342079704,
351581918,
361084132,
366666644,
369142629,
370586346,
376999767,
379519083,
380088560,
389590774,
399092988,
401063805,
408595202,
418097416,
427599630,
437837294,
449600925,
458333305,
468903352,
481276566,
492190172,
493499695,
499999997,
506025444,
549999966,
561489327,
582499964,
609999623,
615237715,
632531805,
641702088,
649999996,
656755941,
676495819,
721914849,
738285258,
759038166,
799999995,
802127610,
805044957,
861332801,
873749946,
875674588,
882340371,
885544527,
889999945,
899201850,
916666661,
937806704,
950227214,
962553132,
974999994,
984380344,
986999390,
1012050888,
1042765893,
1045249354,
1094593235,
1107427887,
1122978654,
1138557249,
1164999928,
1203191415,
1230475430,
1265063610,
1283404176,
1299999992,
1309090901,
1348802775,
1353522973,
1363616937,
1391569971,
1406710056,
1439999911,
1443829698,
1456249910,
1476570516,
1499999999,
1518076332,
1524042459,
1596999013,
1599618059,
1604255220,
1610089914,
1644582693,
1684467981,
1722665602,
1747499892,
1764680742,
1771089054,
1798403700,
1833333322,
1844893503,
1845713145,
1875613408,
1897595415,
1900454428,
1925106264,
1968760688,
1999999999,
2005319025,
2038749874,
2085531786,
2090498708,
2091808231,
2099999987,
2165744547.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 730 values, from 14 to 11402726568).
n\r | 0 | 1 |
2 | 400 | 330 | 2 |
3 | 283 | 223 | 224 | 3 |
4 | 199 | 150 | 201 | 180 | 4 |
5 | 160 | 136 | 144 | 138 | 152 | 5 |
6 | 146 | 95 | 126 | 137 | 128 | 98 | 6 |
7 | 98 | 113 | 107 | 104 | 103 | 101 | 104 | 7 |
8 | 107 | 73 | 98 | 85 | 92 | 77 | 103 | 95 | 8 |
9 | 109 | 83 | 72 | 89 | 70 | 74 | 85 | 70 | 78 | 9 |
10 | 73 | 57 | 82 | 57 | 85 | 87 | 79 | 62 | 81 | 67 | 10 |
11 | 48 | 82 | 64 | 81 | 54 | 61 | 70 | 66 | 66 | 71 | 67 |
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.