The 109 terms in the b-file can be proved to increase without limit on the basis of the existence in each number's trajectory under the map defined in A053392 of a term containing a internal substring of more than two adjacent 9's. Here is a table: Each number is followed by the first term t(n) containing more than two adjacent 9's. This is followed by that term's number of decimal digits. Finally, the adjacent-9's substring(s) and its/their position(s) counting from the left. 1496: t(41) <9089> 999 (7845,7847), (8163,8165) 1497: t(32) <1019> 9999 (720,723) 1498: t(32) <1032> 9999 (720,723) 1499: t(31) <771> 999 (496,498) 1587: t(36) <2412> 999 (753,755) 1588: t(36) <2412> 999 (753,755) 1589: t(36) <2412> 999 (753,755) 1691: t(34) <1032> 9999 (720,723) 1692: t(27) <96> 999 (86,88) 1693: t(27) <96> 999 (86,88) 1694: t(41) <7745> 999 (6206,6208) 1695: t(41) <7773> 999 (6206,6208) 1696: t(38) <3682> 999 (3607,3609) 1697: t(35) <1757> 999 (1684,1686) 1698: t(32) <880> 999 (797,799) 1699: t(32) <876> 999 (797,799) 1719: t(36) <1032> 9999 (720,723) 1728: t(31) <96> 999 (86,88) 1729: t(31) <96> 999 (86,88) 1783: t(37) <175> 999 (35,37) 1784: t(39) <520> 9999 (83,86); 999 (409,411) 1785: t(28) <118> 999 (73,75) 1786: t(28) <159> 999 (73,75) 1787: t(28) <161> 999 (73,75) 1788: t(39) <3138> 999 (1223,1225) 1789: t(36) <1436> 999 (1430,1432) 1791: t(36) <2744> 9999 (720,723); 999 (2389,2391) 1792: t(36) <3056> 9999 (720,723); 999 (2084,2086) 1793: t(32) <876> 999 (797,799) 1794: t(32) <894> 999 (797,799) 1795: t(32) <894> 999 (797,799) 1796: t(40) <8067> 999 (6261,6263), (6474,6476) 1797: t(36) <3726> 999 (3706,3708) 1798: t(37) <4948> 9999 (4792,4795) 1799: t(39) <7721> 999 (6206,6208) 1819: t(56) <2835> 999 (1034,1036) 1867: t(48) <853> 999 (203,205) 1868: t(34) <880> 9999 (227,230) 1869: t(34) <880> 9999 (227,230) 1874: t(38) <1373> 999 (496,498) 1875: t(37) <1722> 999 (639,641) 1876: t(33) <1166> 999 (1146,1148) 1877: t(34) <1618> 9999 (1462,1465) 1878: t(36) <2259> 999 (744,746) 1879: t(36) <2283> 999 (744,746) 1880: t(31) <118> 999 (73,75) 1881: t(31) <159> 999 (73,75) 1882: t(26) <183> 999 (104,106) 1883: t(25) <165> 999 (105,107) 1884: t(26) <220> 999 (149,151) 1885: t(21) <64> 999 (55,57) 1886: t(21) <64> 999 (55,57) 1887: t(30) <711> 999 (514,516) 1888: t(31) <829> 999 (667,669) 1889: t(31) <829> 999 (667,669) 1890: t(30) <810> 999 (496,498) 1891: t(37) <9089> 999 (7845,7847), (8163,8165) 1892: t(28) <1019> 9999 (720,723) 1893: t(28) <1032> 9999 (720,723) 1894: t(27) <771> 999 (496,498) 1895: t(27) <772> 999 (496,498) 1896: t(27) <772> 999 (496,498) 1897: t(27) <810> 999 (496,498) 1898: t(27) <854> 999 (496,498) 1899: t(27) <857> 999 (496,498) 1955: t(41) <2412> 999 (753,755) 1956: t(41) <2412> 999 (753,755) 1957: t(41) <2412> 999 (753,755) 1958: t(40) <1513> 999 (414,416), (1305,1307) 1959: t(27) <83> 999 (12,14) 1964: t(40) <2510> 999 (1923,1925) 1965: t(32) <1029> 999 (926,928) 1966: t(37) <3664> 999 (3266,3268) 1967: t(36) <2844> 999 (1248,1250) 1968: t(39) <7292> 999 (431,433) 1969: t(35) <2777> 9999 (2478,2481) 1970: t(27) <123> 999 (56,58) 1971: t(27) <125> 999 (56,58) 1972: t(27) <128> 999 (56,58) 1973: t(28) <323> 999 (212,214) 1974: t(28) <377> 999 (212,214) 1975: t(24) <123> 999 (56,58) 1976: t(24) <125> 999 (56,58) 1977: t(24) <128> 999 (56,58) 1978: t(33) <1335> 999 (696,698), (900,902) 1979: t(33) <1417> 999 (696,698) 1980: t(35) <2412> 999 (753,755) 1981: t(35) <2412> 999 (753,755) 1982: t(27) <314> 999 (145,147) 1983: t(28) <549> 999 (470,472) 1984: t(27) <451> 999 (391,393) 1985: t(28) <577> 999 (506,508) 1986: t(23) <165> 999 (156,158) 1987: t(23) <165> 999 (156,158) 1988: t(32) <1736> 999 (417,419), (1539,1541) 1989: t(32) <1681> 999 (417,419) 1991: t(27) <628> 999 (202,204) 1992: t(27) <628> 999 (202,204) 1993: t(27) <628> 999 (202,204) 1994: t(27) <628> 999 (202,204) 1995: t(27) <628> 999 (202,204) 1996: t(27) <628> 999 (202,204) 1997: t(27) <628> 999 (202,204) 1998: t(27) <628> 999 (202,204) 1999: t(27) <628> 999 (202,204) 2496: t(36) <2412> 999 (753,755) 2497: t(36) <2412> 999 (753,755) 2498: t(36) <2412> 999 (753,755) 2499: t(36) <2412> 999 (753,755)