Search a number
gapful numbers
A number divisible by the number formed by its first and last digit. more

The first 600 gapful numbers :
100, 105, 108, 110, 120, 121, 130, 132, 135, 140, 143, 150, 154, 160, 165, 170, 176, 180, 187, 190, 192, 195, 198, 200, 220, 225, 231, 240, 242, 253, 260, 264, 275, 280, 286, 297, 300, 315, 330, 341, 352, 360, 363, 374, 385, 390, 396, 400, 405, 440, 451, 462, 473, 480, 484, 495, 500, 550, 561, 572, 583, 594, 600, 660, 671, 682, 693, 700, 770, 781, 792, 800, 880, 891, 900, 990, 1000, 1001, 1005, 1008, 1010, 1020, 1030, 1032, 1035, 1037, 1040, 1050, 1053, 1056, 1060, 1064, 1065, 1070, 1080, 1090, 1092, 1095, 1098, 1100, 1110, 1111, 1120, 1125, 1130, 1134, 1136, 1140, 1150, 1152, 1155, 1159, 1160, 1170, 1180, 1183, 1185, 1188, 1190, 1200, 1204, 1207, 1210, 1212, 1215, 1216, 1220, 1221, 1230, 1240, 1245, 1250, 1260, 1270, 1272, 1274, 1275, 1278, 1280, 1290, 1296, 1300, 1305, 1310, 1313, 1320, 1330, 1331, 1332, 1335, 1340, 1344, 1349, 1350, 1360, 1365, 1368, 1370, 1376, 1377, 1380, 1390, 1392, 1395, 1400, 1410, 1414, 1420, 1425, 1430, 1440, 1441, 1443, 1450, 1452, 1455, 1456, 1458, 1460, 1470, 1480, 1484, 1485, 1490, 1500, 1510, 1512, 1515, 1520, 1530, 1536, 1539, 1540, 1545, 1547, 1548, 1550, 1551, 1554, 1560, 1570, 1572, 1573, 1575, 1580, 1590, 1600, 1605, 1610, 1616, 1620, 1624, 1630, 1632, 1635, 1638, 1640, 1650, 1660, 1661, 1665, 1670, 1680, 1690, 1692, 1694, 1695, 1696, 1700, 1703, 1710, 1717, 1720, 1725, 1728, 1729, 1730, 1740, 1750, 1752, 1755, 1760, 1764, 1770, 1771, 1776, 1780, 1785, 1790, 1800, 1810, 1812, 1815, 1818, 1820, 1830, 1833, 1834, 1840, 1845, 1850, 1856, 1860, 1870, 1872, 1875, 1880, 1881, 1887, 1890, 1900, 1904, 1905, 1908, 1910, 1919, 1920, 1930, 1932, 1935, 1936, 1940, 1950, 1960, 1963, 1965, 1970, 1974, 1980, 1990, 1991, 1992, 1995, 1998, 2000, 2002, 2020, 2025, 2040, 2059, 2060, 2064, 2075, 2080, 2093, 2100, 2106, 2112, 2120, 2121, 2125, 2128, 2140, 2160, 2175, 2180, 2184, 2187, 2200, 2220, 2222, 2225, 2236, 2240, 2260, 2268, 2275, 2280, 2300, 2304, 2320, 2323, 2325, 2331, 2332, 2340, 2349, 2360, 2366, 2375, 2380, 2400, 2408, 2420, 2424, 2425, 2440, 2442, 2457, 2460, 2475, 2480, 2496, 2500, 2520, 2525, 2540, 2541, 2544, 2548, 2552, 2553, 2560, 2575, 2580, 2600, 2620, 2625, 2626, 2639, 2640, 2660, 2662, 2664, 2675, 2680, 2688, 2700, 2720, 2725, 2727, 2740, 2751, 2756, 2760, 2772, 2775, 2780, 2783, 2784, 2800, 2820, 2825, 2828, 2840, 2860, 2875, 2880, 2882, 2886, 2900, 2904, 2920, 2925, 2929, 2940, 2960, 2961, 2968, 2975, 2980, 2992, 2997, 3000, 3003, 3030, 3045, 3060, 3072, 3078, 3090, 3094, 3096, 3115, 3120, 3131, 3150, 3159, 3180, 3185, 3210, 3232, 3240, 3255, 3264, 3268, 3270, 3276, 3300, 3325, 3330, 3333, 3360, 3367, 3390, 3392, 3395, 3420, 3434, 3441, 3450, 3456, 3458, 3465, 3480, 3510, 3535, 3540, 3549, 3552, 3570, 3600, 3604, 3605, 3630, 3636, 3648, 3660, 3663, 3675, 3690, 3712, 3720, 3737, 3745, 3750, 3751, 3774, 3780, 3810, 3815, 3816, 3838, 3840, 3870, 3872, 3885, 3900, 3930, 3939, 3944, 3955, 3960, 3990, 3993, 3996, 4000, 4004, 4005, 4032, 4040, 4080, 4095, 4120, 4128, 4141, 4160, 4185, 4186, 4200, 4224, 4240, 4242, 4275, 4277, 4280, 4320, 4343, 4360, 4365, 4368, 4400, 4416, 4440, 4444, 4452, 4455, 4459, 4480, 4520, 4545, 4551, 4560, 4600, 4608, 4635, 4640, 4646, 4662, 4664, 4680, 4720, 4725, 4747, 4760, 4773, 4800, 4815, 4840, 4848, 4872, 4876, 4880, 4884, 4905, 4920, 4949, 4960, 4961, 4995, 5000, 5005, 5050, 5096, 5100, 5115, 5150, 5151, 5184, 5187, 5200, 5225, 5250, 5252, 5278, 5300, 5335, 5350, 5353, 5369, 5376, 5400, 5445, 5450, 5454, 5500, 5512, 5550, 5555, 5568, 5600, 5650, 5656, 5661, 5665, 5700, 5724, 5750, 5757, 5772.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 74623687 values, from 100 to 1000000000).

n\r 0  1 
25176723022856457 2 
3400329891729536117295337 3 
436835353114282221493187711428235 4 
5440247297844198804162972745687438563 5 
62675547847894751250586613277511125058864789471 6 
717664603949317594931889493174949317094931819493196 7 
82300548257141087465934571412713829871571411474659435714108 8 
9172632865765136576511411384842576510357651141138486157651225765109 9 
10314329972984424569246927244615231883125917324859774234916045501072206680 10 
11110729616355062635504663550796355059635507463550796355079635508263550906355076

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.