Pairs of elements
Lexicographically earliest infinite succession S of distinct pairs of
elements a and b such that a>b (a and b being respectively terms or
digits of S).
S = 1,0,3,2,5,4,7,6,9,8,20,10,30,21,32,31,41,40,43,42,51,50,53,52,60,54,62,61,64,63,70,65,72,71,74,73,76,75,81,80,83,82,85,84,87,86,91,90,93,92,95,94,97,96,102,12,14,13,16,15,18,17,22,19,24,23,26,25,28,27,33,29,44,34,36,35,38,37,45,39,...
Let us materialize the pairs of terms of S (grey and yellow pairs):
S = 1,0,3,2,5,4,7,6,9,8,20,10,30,21,32,31,41,40,43,42,51,50,53,52,60,54,62,61,64,63,70,65,72,71,74,73,76,75,81,80,83,82,85,84,87,86,91,90,93,92,95,94,97,96,102,12,14,13,16,15,18,17,22,19,24,23,26,25,28,27,33,29,44,34,36,35,38,37,45,39,...
We see that the first term of any yellow or grey pair is larger than the second one.
Let us materialize the pairs of digits of S (grey and yellow pairs):
S = 1,0,3,2,5,4,7,6,9,8,20,10,30,21,32,31,41,40,43,42,51,50,53,52,60,54,62,61,64,63,70,65,72,71,74,73,76,75,81,80,83,82,85,84,87,86,91,90,93,92,95,94,97,96,102,12,14,13,16,15,18,17,22,19,24,23,26,25,28,27,33,29,44,34,36,35,38,37,45,39,...
We see that the first digit in any yellow or grey pair is larger than the second one.
This was tough to compute by hand – please forgive the typos, errors, etc.
I suspect a great and interesting graph for S!
____________________
Next day update
Jean-Marc Falcoz was quick to correct and extend S (graph at the bottom of the page):
> s1264={1,0,3,2,5,4,7,6,9,8,20,10,30,21,32,31,41,40,43,42,51,50,53,52,60,54,62,61,64,63,70,65,72,71,74,73,76,75,81,80,83,82,85,84,87,86,91,90,93,92,95,94,97,96,102,12,14,13,16,15,18,17,22,19,24,23,26,25,28,27,33,29,35,34,37,36,39,38,45,44,110,98,105,46,48,47,55,49,57,56,59,58,67,66,120,103,121,104,130,106,131,107,69,68,78,77,132,108,140,109,88,79,210,202,1102,141,203,142,204,143,205,150,206,151,207,152,208,153,209,89,220,212,1103,154,213,160,214,161,215,162,216,163,217,164,218,165,219,170,302,171,303,172,304,173,305,174,306,175,307,176,308,180,309,181,312,182,313,183,314,184,315,185,316,186,317,187,318,190,319,191,322,192,323,193,324,194,325,195,326,196,327,197,328,198,329,221,403,230,404,231,405,232,406,240,407,241,408,242,409,243,413,250,414,251,415,252,416,253,417,254,418,260,419,261,423,262,424,263,425,264,426,265,427,270,428,271,429,272,433,273,434,274,435,275,436,276,437,280,438,281,439,282,503,283,504,284,505,285,506,286,507,287,508,290,509,291,513,292,514,293,515,294,516,295,517,296,518,297,519,298,524,310,525,320,526,321,527,330,528,331,529,332,534,340,535,341,536,342,537,343,538,350,539,351,544,352,545,353,546,354,547,360,548,361,549,362,604,363,605,364,606,365,607,370,608,371,609,372,614,373,615,374,616,375,617,376,618,380,619,381,624,382,625,383,626,384,627,385,628,386,629,387,634,390,635,391,636,392,637,393,638,394,639,395,644,396,645,397,646,398,647,410,648,420,649,421,655,430,656,431,657,432,658,440,659,441,705,442,706,443,707,450,708,451,709,452,715,453,716,454,717,460,718,461,719,462,725,463,726,464,727,465,728,470,729,471,735,472,736,473,737,474,738,475,739,476,745,480,746,481,747,482,748,483,749,484,755,485,756,486,757,487,758,490,759,491,765,492,766,493,767,494,768,495,769,496,805,497,806,498,807,510,808,520,809,521,816,530,817,531,818,532,819,540,826,541,827,542,828,543,829,550,836,551,837,552,838,553,839,554,846,560,847,561,848,562,849,563,856,564,857,565,858,570,859,571,866,572,867,573,868,574,869,575,876,576,877,580,878,581,879,582,906,583,907,584,908,585,909,586,916,587,917,590,918,591,919,592,926,593,927,594,928,595,929,596,936,597,937,598,938,610,939,620,947,621,948,630,949,631,957,632,958,640,959,641,967,642,968,643,969,650,977,651,978,652,979,653,987,654,988,660,989,661,1010,402,1105,1104,1107,662,1020,412,1108,663,1021,422,1109,664,1030,502,1202,1106,1204,1203,1206,1205,1207,665,1031,512,1208,670,1032,522,1209,671,1040,523,1213,1212,1215,1214,1217,672,1041,533,1218,673,1042,602,1219,674,1043,603,1302,1216,1304,1303,1306,1305,1307,675,1050,612,1308,676,1051,613,1309,680,1052,622,1313,1312,1315,1314,1317,681,1053,623,1318,682,1054,633,1319,683,1060,702,1322,1316,1324,1323,1326,1325,1327,684,1061,703,1328,685,1062,704,1329,686,1063,712,1403,1402,1405,1404,1407,687,1064,713,1408,690,1065,714,1409,691,1070,722,1412,1406,1414,1413,1416,1415,1417,692,1071,723,1418,693,1072,724,1419,694,1073,732,1423,1422,1425,1424,1427,695,1074,733,1428,696,1075,734,1429,697,1076,742,1432,1426,1434,1433,1436,1435,1437,698,1080,743,1438,710,1081,744,1439,720,1082,752,1503,1502,1505,1504,1507,1506,1508,721,1083,753,1509,730,1084,754,1513,1512,1515,1514,1517,1516,1518,731,1085,762,1519,740,1086,763,1523,1522,1525,1524,1527,1526,1528,741,1087,764,1529,750,1090,802,1533,1532,1535,1534,1537,1536,1538,751,1091,803,1539,760,1092,804,1543,1542,1545,1544,1547,1546,1548,761,1093,812,1549,770,1094,813,1603,1602,1605,1604,1607,1606,1608,771,1095,814,1609,772,1096,815,1613,1612,1615,1614,1617,1616,1618,773,1097,822,1619,774,1098,823,1623,1622,1625,1624,1627,1626,1628,775,2010,824,1629,776,2020,825,1633,1632,1635,1634,1637,1636,1638,780,2021,832,1639,781,2030,833,1643,1642,1645,1644,1647,1646,1648,782,2031,834,1649,783,2032,835,1653,1652,1655,1654,1657,1656,1658,784,2040,842,1659,785,2041,843,1703,1702,1705,1704,1707,1706,1708,786,2042,844,1709,787,2043,845,1713,1712,1715,1714,1717,1716,1718,790,2050,852,1719,791,2051,853,1723,1722,1725,1724,1727,1726,1728,792,2052,854,1729,793,2053,855,1733,1732,1735,1734,1737,1736,1738,794,2054,862,1739,795,2060,863,1743,1742,1745,1744,1747,1746,1748,796,2061,864,1749,797,2062,865,1753,1752,1755,1754,1757,1756,1758,798,2063,872,1759,810,2064,873,1763,1762,1765,1764,1767,1766,1769,820,2065,874,1802,1768,1804,1803,1806,1805,1808,1807,1809,821,2070,875,1813,1812,1815,1814,1817,1816,1819,830,2071,902,1822,1818,1824,1823,1826,1825,1828,1827,1829,831,2072,903,1833,1832,1835,1834,1837,1836,1839,840,2073,904,1842,1838,1844,1843,1846,1845,1848,1847,1849,841,2074,905,1853,1852,1855,1854,1857,1856,1859,850,2075,912,1862,1858,1864,1863,1866,1865,1868,1867,1869,851,2076,913,1873,1872,1875,1874,1877,1876,1879,860,2080,914,1902,1878,1904,1903,1906,1905,1908,1907,1909,861,2081,915,1913,1912,1915,1914,1917,1916,1919,870,2082,922,1922,1918,1924,1923,1926,1925,1928,1927,1929,871,2083,923,1933,1932,1935,1934,1937,1936,1939,880,2084,924,1942,1938,1944,1943,1946,1945,1948,1947,1949,881,2085,925,1953,1952,1955,1954,1957,1956,1959,882,2086,932,1962,1958,1964,1963,1966,1965,1968,1967,1969,883,2087,933,1973,1972,1975,1974,1977,1976,1979,884,2090,934,1982,1978,1984,1983,1986,1985,1988,1987,1989,885,2091,935,2103,2102,11010,942,11020,943,2105,2104,2107,2106,2109,886,2092,944,2203,2108,2204,2202,11021,945,2206,2205,2208,2207,2209,887,2093,946,2213,2212,11030,952,11031,953,2215,2214,2217,2216,2219,890,2094,954,2303,2218,2304,2302,11032,955,2306,2305,2308,2307,2309,891,2095,956,2313,2312,11040,962,11041,963,2315,2314,2317,2316,2319,892,2096,964,2323,2318,2324,2322}
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