A curious circuit

During our latest space mission to Mars, humankind has retrieved a curious alien circuit. Our historians think it must be a calendar of some sort.

After speaking with some alien linguists, we know now that the characters are symbols of counting and we deduced that they must be numbers.

When the engineering deparment hooked up the circuit to a low-frequency signal, it started moving, emitting light and spitting out similar symbols. Freely translated, the engineers observed and wrote down the following sequence

[2, 1], [5, 5], [8, 2], [11, 1], [14, 5], [15, 4], [18, 3], [21, 2], [22, 3], [25, 2], [28, 1], [31, 5], [34, 2], [37, 1], [40, 5], [43, 2], [46, 1], [49, 5], [50, 4], [51, 2], [52, 3], [55, 2], [58, 1], [61, 5], [64, 2], [67, 1], [70, 5], [71, 4], [74, 3], [77, 2], [80, 1], [81, 2], [82, 3], [85, 2], [88, 1], [91, 5], [92, 4], [93, 2], [94, 3], [97, 2], [100, 1], [101, 2], [104, 1], [107, 5], [110, 2], [113, 1], [116, 5], [119, 2], [122, 1], [125, 5], [128, 2], [131, 1], [134, 5], [137, 2], [140, 1], [141, 2], [142, 3], [145, 2], [148, 1], [151, 5], [154, 2], [157, 1], [160, 5], [163, 2], [166, 1], [169, 5], [172, 2], [175, 1], [176, 2], [179, 1], [182, 5], [183, 4], [186, 3], [189, 2], [190, 3], [191, 5], [194, 2], [197, 1], [200, 5], [203, 2], [206, 1], [209, 5], [212, 2], [215, 1], [216, 2], [217, 3], [220, 2], [223, 1], [226, 5], [229, 2], [232, 1], [235, 5], [238, 2], [241, 1], [244, 5], [247, 2], [250, 1], [251, 2], [254, 1], [257, 5], [260, 2], [263, 1], [266, 5], [267, 4], [270, 3], [271, 5], [274, 2], [277, 1], [280, 5], [281, 4], [284, 3], [287, 2], [290, 1], [291, 2], [292, 3], [295, 2], [298, 1], [301, 5], [302, 4], [303, 2], [304, 3], [307, 2], [310, 1], [311, 2], [314, 1], [317, 5], [320, 2], [323, 1], [326, 5], [329, 2], [332, 1], [335, 5], [338, 2], [341, 1], [344, 5], [347, 2], [350, 1], [351, 2], [352, 3], [355, 2], [358, 1], [361, 5], [364, 2], [367, 1], [370, 5], [373, 2], [376, 1], [379, 5], [382, 2], [385, 1], [386, 2], [389, 1], [392, 5], [393, 4], [396, 3], [399, 2], [400, 3], [401, 5], [404, 2], [407, 1], [410, 5], [413, 2], [416, 1], [419, 5], [422, 2], [425, 1], [426, 2], [427, 3], [430, 2], [433, 1], [436, 5], [439, 2], [442, 1], [445, 5], [448, 2], [451, 1], [454, 5], [457, 2], [460, 1], [461, 2], [464, 1], [467, 5], [470, 2], [473, 1], [476, 5], [477, 4], [480, 3], [481, 5], [484, 2], [487, 1], [490, 5], [491, 4], [494, 3], [497, 2], [500, 1], [501, 2], [502, 3], [505, 2], [508, 1], [511, 5], [512, 4], [513, 2], [514, 3], [517, 2], [520, 1], [521, 2], [524, 1], [527, 5], [530, 2], [533, 1], [536, 5], [539, 2], [542, 1], [545, 5], [548, 2], [551, 1], [554, 5], [557, 2], [560, 1], [561, 2], [562, 3], [565, 2], [568, 1], [571, 5], [574, 2], [577, 1], [580, 5], [583, 2], [586, 1], [589, 5], [592, 2], [595, 1], [596, 2], [599, 1], [602, 5], [603, 4], [606, 3], [609, 2], [610, 3], [611, 5], [614, 2], [617, 1], [620, 5], [623, 2], [626, 1], [629, 5], [632, 2], [635, 1], [636, 2], [637, 3], [640, 2], [643, 1], [646, 5], [649, 2], [652, 1], [655, 5], [658, 2], [661, 1], [664, 5], [667, 2], [670, 1], [671, 2], [674, 1], [677, 5], [680, 2], [683, 1], [686, 5], [687, 4], [690, 3], [691, 5], [694, 2], [697, 1], [700, 5], [701, 4], [704, 3], [707, 2], [710, 1], [711, 2], [712, 3], [715, 2], [718, 1], [721, 5], [722, 4], [723, 2], [724, 3], [727, 2], [730, 1], [731, 2], [734, 1], [737, 5], [740, 2], [743, 1], [746, 5], [749, 2], [752, 1], [755, 5], [758, 2], [761, 1], [764, 5], [767, 2], [770, 1], [771, 2], [772, 3], [775, 2], [778, 1], [781, 5], [784, 2], [787, 1], [790, 5], [793, 2], [796, 1], [799, 5], [802, 2], [805, 1], [806, 2], [809, 1], [812, 5], [813, 4], [816, 3], [819, 2], [820, 3], [821, 5], [824, 2], [827, 1], [830, 5], [833, 2], [836, 1], [839, 5], [842, 2], [845, 1], [846, 2], [847, 3], [850, 2], [853, 1], [856, 5], [859, 2], [862, 1], [865, 5], [868, 2], [871, 1], [874, 5], [877, 2], [880, 1], [881, 2], [884, 1], [887, 5], [890, 2], [893, 1], [896, 5], [897, 4], [900, 3], [901, 5], [904, 2], [907, 1], [910, 5], [911, 4], [914, 3], [917, 2], [920, 1], [921, 2], [922, 3], [925, 2], [928, 1], [931, 5], [932, 4], [933, 2], [934, 3], [937, 2], [940, 1], [941, 2], [944, 1], [947, 5], [950, 2], [953, 1], [956, 5], [959, 2], [962, 1], [965, 5], [968, 2], [971, 1], [974, 5], [977, 2], [980, 1], [981, 2], [982, 3], [985, 2], [988, 1], [991, 5], [994, 2], [997, 1], [1000, 5], [1003, 2], [1006, 1], [1009, 5], [1012, 2], [1015, 1], [1016, 2], [1019, 1], [1022, 5], [1023, 4], [1026, 3], [1029, 2], [1030, 3], [1031, 5], [1034, 2], [1037, 1], [1040, 5], [1043, 2], [1046, 1], [1049, 5], [1052, 2], [1055, 1], [1056, 2], [1057, 3], [1060, 2], [1063, 1], [1066, 5], [1069, 2], [1072, 1], [1075, 5], [1078, 2], [1081, 1], [1084, 5], [1087, 2], [1090, 1], [1091, 2], [1094, 1], [1097, 5], [1100, 2], [1103, 1], [1106, 5], [1107, 4], [1110, 3], [1111, 5], [1114, 2], [1117, 1], [1120, 5], [1121, 4], [1124, 3], [1127, 2], [1130, 1], [1131, 2], [1132, 3], [1135, 2], [1138, 1], [1141, 5], [1142, 4], [1143, 2], [1144, 3], [1147, 2], [1150, 1], [1151, 2], [1154, 1], [1157, 5], [1160, 2], [1163, 1], [1166, 5], [1169, 2], [1172, 1], [1175, 5], [1178, 2], [1181, 1], [1184, 5], [1187, 2], [1190, 1], [1191, 2], [1192, 3], [1195, 2], [1198, 1], [1201, 5], [1204, 2], [1207, 1], [1210, 5], [1213, 2], [1216, 1], [1219, 5], [1222, 2], [1225, 1], [1226, 2], [1229, 1], [1232, 5], [1233, 4], [1236, 3], [1239, 2], [1240, 3], [1241, 5], [1244, 2], [1247, 1], [1250, 5], [1253, 2], [1256, 1], [1259, 5], [1262, 2], [1265, 1], [1266, 2], [1267, 3], [1270, 2], [1273, 1], [1276, 5], [1279, 2], [1282, 1], [1285, 5], [1288, 2], [1291, 1], [1294, 5], [1297, 2], [1300, 1], [1301, 2], [1304, 1], [1307, 5], [1310, 2], [1313, 1], [1316, 5], [1317, 4], [1320, 3], [1321, 5], [1324, 2], [1327, 1], [1330, 5], [1331, 4], [1334, 3], [1337, 2], [1340, 1], [1341, 2], [1342, 3], [1345, 2], [1348, 1], [1351, 5], [1352, 4], [1353, 2], [1354, 3], [1357, 2], [1360, 1], [1361, 2], [1364, 1], [1367, 5], [1370, 2], [1373, 1], [1376, 5], [1379, 2], [1382, 1], [1385, 5], [1388, 2], [1391, 1], [1394, 5], [1397, 2], [1400, 1], [1401, 2], [1402, 3], [1405, 2], [1408, 1], [1411, 5], [1414, 2], [1417, 1], [1420, 5], [1423, 2], [1426, 1], [1429, 5], [1432, 2], [1435, 1], [1436, 2], [1439, 1], [1442, 5], [1443, 4], [1446, 3], [1449, 2], [1450, 3], [1451, 5], [1454, 2], [1457, 1], [1460, 5], [1463, 2], [1466, 1], [1469, 5], [1472, 2], [1475, 1], [1476, 2], [1477, 3], [1480, 2], [1483, 1], [1486, 5], [1489, 2], [1492, 1], [1495, 5], [1498, 2], [1501, 1], [1504, 5], [1507, 2], [1510, 1], [1511, 2], [1514, 1], [1517, 5], [1520, 2], [1523, 1], [1526, 5], [1527, 4], [1530, 3], [1531, 5], [1534, 2], [1537, 1], [1540, 5], [1541, 4], [1544, 3], [1547, 2], [1550, 1], [1551, 2], [1552, 3], [1555, 2], [1558, 1], [1561, 5], [1562, 4], [1563, 2], [1564, 3], [1567, 2], [1570, 1], [1571, 2], [1574, 1], [1577, 5], [1580, 2], [1583, 1], [1586, 5], [1589, 2], [1592, 1], [1595, 5], [1598, 2], [1601, 1], [1604, 5], [1607, 2], [1610, 1], [1611, 2], [1612, 3], [1615, 2], [1618, 1], [1621, 5], [1624, 2], [1627, 1], [1630, 5], [1633, 2], [1636, 1], [1639, 5], [1642, 2], [1645, 1], [1646, 2], [1649, 1], [1652, 5], [1653, 4], [1656, 3], [1659, 2], [1660, 3], [1661, 5], [1664, 2], [1667, 1], [1670, 5], [1673, 2], [1676, 1], [1679, 5], [1682, 2], [1685, 1], [1686, 2], [1687, 3], [1690, 2], [1693, 1], [1696, 5], [1699, 2], [1702, 1], [1705, 5], [1708, 2], [1711, 1], [1714, 5], [1717, 2], [1720, 1], [1721, 2], [1724, 1], [1727, 5], [1730, 2], [1733, 1], [1736, 5], [1737, 4], [1740, 3], [1741, 5], [1744, 2], [1747, 1], [1750, 5], [1751, 4], [1754, 3], [1757, 2], [1760, 1], [1761, 2], [1762, 3], [1765, 2], [1768, 1], [1771, 5], [1772, 4], [1773, 2], [1774, 3], [1777, 2], [1780, 1], [1781, 2], [1784, 1], [1787, 5], [1790, 2], [1793, 1], [1796, 5], [1799, 2], [1802, 1], [1805, 5], [1808, 2], [1811, 1], [1814, 5], [1817, 2], [1820, 1], [1821, 2], [1822, 3], [1825, 2], [1828, 1], [1831, 5], [1834, 2], [1837, 1], [1840, 5], [1843, 2], [1846, 1], [1849, 5], [1852, 2], [1855, 1], [1856, 2], [1859, 1], [1862, 5], [1863, 4], [1866, 3], [1869, 2], [1870, 3], [1871, 5], [1874, 2], [1877, 1], [1880, 5], [1883, 2], [1886, 1], [1889, 5], [1892, 2], [1895, 1], [1896, 2], [1897, 3], [1900, 2], [1903, 1], [1906, 5], [1909, 2], [1912, 1], [1915, 5], [1918, 2], [1921, 1], [1924, 5], [1927, 2], [1930, 1], [1931, 2], [1934, 1], [1937, 5], [1940, 2], [1943, 1], [1946, 5], [1947, 4], [1950, 3], [1951, 5], [1954, 2], [1957, 1], [1960, 5], [1961, 4], [1964, 3], [1967, 2], [1970, 1], [1971, 2], [1972, 3], [1975, 2], [1978, 1], [1981, 5], [1982, 4], [1983, 2], [1984, 3], [1987, 2], [1990, 1], [1991, 2], [1994, 1], [1997, 5], [2000, 2], [2003, 1], [2006, 5], [2009, 2], [2012, 1], [2015, 5], [2018, 2], [2021, 1], [2024, 5], [2027, 2], [2030, 1], [2031, 2], [2032, 3], [2035, 2], [2038, 1], [2041, 5], [2044, 2], [2047, 1], [2050, 5], [2053, 2], [2056, 1], [2059, 5], [2062, 2], [2065, 1], [2066, 2], [2069, 1], [2072, 5], [2073, 4], [2076, 3], [2079, 2], [2080, 3], [2081, 5], [2084, 2], [2087, 1], [2090, 5], [2093, 2], [2096, 1], [2099, 5], [2102, 2], [2105, 1], [2106, 2], [2107, 3], [2110, 2], [2113, 1], [2116, 5], [2119, 2], [2122, 1], [2125, 5], [2128, 2], [2131, 1], [2134, 5], [2137, 2], [2140, 1], [2141, 2], [2144, 1], [2147, 5], [2150, 2], [2153, 1], [2156, 5], [2157, 4], [2160, 3], [2161, 5], [2164, 2], [2167, 1], [2170, 5], [2171, 4], [2174, 3], [2177, 2], [2180, 1], [2181, 2], [2182, 3], [2185, 2], [2188, 1], [2191, 5], [2192, 4], [2193, 2], [2194, 3], [2197, 2], [2200, 1], [2201, 2], [2204, 1], [2207, 5], [2210, 2], [2213, 1], [2216, 5], [2219, 2], [2222, 1], [2225, 5], [2228, 2], [2231, 1], [2234, 5], [2237, 2], [2240, 1], [2241, 2], [2242, 3], [2245, 2], [2248, 1], [2251, 5], [2254, 2], [2257, 1], [2260, 5], [2263, 2], [2266, 1], [2269, 5], [2272, 2], [2275, 1], [2276, 2], [2279, 1], [2282, 5], [2283, 4], [2286, 3], [2289, 2], [2290, 3], [2291, 5], [2294, 2], [2297, 1], [2300, 5], [2303, 2], [2306, 1], [2309, 5], [2312, 2], [2315, 1], [2316, 2], [2317, 3], [2320, 2], [2323, 1], [2326, 5], [2329, 2], [2332, 1], [2335, 5], [2338, 2], [2341, 1], [2344, 5], [2347, 2], [2350, 1], [2351, 2], [2354, 1], [2357, 5], [2360, 2], [2363, 1], [2366, 5], [2367, 4], [2370, 3], [2371, 5], [2374, 2], [2377, 1], [2380, 5], [2381, 4], [2384, 3], [2387, 2], [2390, 1], [2391, 2], [2392, 3], [2395, 2], [2398, 1], [2401, 5], [2402, 4], [2403, 2], [2404, 3], [2407, 2], [2410, 1], [2411, 2], [2414, 1], [2417, 5], [2420, 2], [2423, 1], [2426, 5], [2429, 2], [2432, 1], [2435, 5], [2438, 2], [2441, 1], [2444, 5], [2447, 2], [2450, 1], [2451, 2], [2452, 3], [2455, 2], [2458, 1], [2461, 5], [2464, 2], [2467, 1], [2470, 5], [2473, 2], [2476, 1], [2479, 5], [2482, 2], [2485, 1], [2486, 2], [2489, 1], [2492, 5], [2493, 4], [2496, 3], [2499, 2], [2500, 3], [2501, 5], [2504, 2], [2507, 1], [2510, 5], [2513, 2], [2516, 1], [2519, 5], [2522, 2], [2525, 1], [2526, 2], [2527, 3], [2530, 2], [2533, 1], [2536, 5], [2539, 2], [2542, 1], [2545, 5], [2548, 2], [2551, 1], [2554, 5], [2557, 2], [2560, 1]

before the circuit broke down. The sequence has the format [output, state number/light]. When we analyzed the parts, we could see some circular objects looking similar but with different sizes.

Can we determine how the circuit worked and recreate a functioning one using human technology? A solution should at least describe the rule how the numbers of generated.