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fibodiv numbers
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 
2400330 2 
3283223224 3 
4199150201180 4 
5160136144138152 5 
61469512613712898 6 
798113107104103101104 7 
8107739885927710395 8 
91098372897074857078 9 
1073578257858779628167 10 
114882648154617066667167

A pictorial representation of the table above
motab
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.