[seqfan] Re: Concatenate the sums of the neighboring digits
Hans Havermann
gladhobo at bell.net
Sat Nov 2 21:46:08 CET 2019
HH: "Roughly (I just iterated numbers 50 times and noted large final terms): ..."
The 109 terms I provided may be said to increase without limit on the basis of the existence in each number's repeated application of the map defined in A053392 a term containing a strictly internal substring of more than two adjacent 9's. Here is a table:
1496: a(41) <9089> 999 (7845,7847), (8163,8165)
1497: a(32) <1019> 9999 (720,723)
1498: a(32) <1032> 9999 (720,723)
1499: a(31) <771> 999 (496,498)
1587: a(36) <2412> 999 (753,755)
1588: a(36) <2412> 999 (753,755)
1589: a(36) <2412> 999 (753,755)
1691: a(34) <1032> 9999 (720,723)
1692: a(27) <96> 999 (86,88)
1693: a(27) <96> 999 (86,88)
1694: a(41) <7745> 999 (6206,6208)
1695: a(41) <7773> 999 (6206,6208)
1696: a(38) <3682> 999 (3607,3609)
1697: a(35) <1757> 999 (1684,1686)
1698: a(32) <880> 999 (797,799)
1699: a(32) <876> 999 (797,799)
1719: a(36) <1032> 9999 (720,723)
1728: a(31) <96> 999 (86,88)
1729: a(31) <96> 999 (86,88)
1783: a(37) <175> 999 (35,37)
1784: a(39) <520> 9999 (83,86); 999 (409,411)
1785: a(28) <118> 999 (73,75)
1786: a(28) <159> 999 (73,75)
1787: a(28) <161> 999 (73,75)
1788: a(39) <3138> 999 (1223,1225)
1789: a(36) <1436> 999 (1430,1432)
1791: a(36) <2744> 9999 (720,723); 999 (2389,2391)
1792: a(36) <3056> 9999 (720,723); 999 (2084,2086)
1793: a(32) <876> 999 (797,799)
1794: a(32) <894> 999 (797,799)
1795: a(32) <894> 999 (797,799)
1796: a(40) <8067> 999 (6261,6263), (6474,6476)
1797: a(36) <3726> 999 (3706,3708)
1798: a(37) <4948> 9999 (4792,4795)
1799: a(39) <7721> 999 (6206,6208)
1819: a(56) <2835> 999 (1034,1036)
1867: a(48) <853> 999 (203,205)
1868: a(34) <880> 9999 (227,230)
1869: a(34) <880> 9999 (227,230)
1874: a(38) <1373> 999 (496,498)
1875: a(37) <1722> 999 (639,641)
1876: a(33) <1166> 999 (1146,1148)
1877: a(34) <1618> 9999 (1462,1465)
1878: a(36) <2259> 999 (744,746)
1879: a(36) <2283> 999 (744,746)
1880: a(31) <118> 999 (73,75)
1881: a(31) <159> 999 (73,75)
1882: a(26) <183> 999 (104,106)
1883: a(25) <165> 999 (105,107)
1884: a(26) <220> 999 (149,151)
1885: a(21) <64> 999 (55,57)
1886: a(21) <64> 999 (55,57)
1887: a(30) <711> 999 (514,516)
1888: a(31) <829> 999 (667,669)
1889: a(31) <829> 999 (667,669)
1890: a(30) <810> 999 (496,498)
1891: a(37) <9089> 999 (7845,7847), (8163,8165)
1892: a(28) <1019> 9999 (720,723)
1893: a(28) <1032> 9999 (720,723)
1894: a(27) <771> 999 (496,498)
1895: a(27) <772> 999 (496,498)
1896: a(27) <772> 999 (496,498)
1897: a(27) <810> 999 (496,498)
1898: a(27) <854> 999 (496,498)
1899: a(27) <857> 999 (496,498)
1955: a(41) <2412> 999 (753,755)
1956: a(41) <2412> 999 (753,755)
1957: a(41) <2412> 999 (753,755)
1958: a(40) <1513> 999 (414,416), (1305,1307)
1959: a(27) <83> 999 (12,14)
1964: a(40) <2510> 999 (1923,1925)
1965: a(32) <1029> 999 (926,928)
1966: a(37) <3664> 999 (3266,3268)
1967: a(36) <2844> 999 (1248,1250)
1968: a(39) <7292> 999 (431,433)
1969: a(35) <2777> 9999 (2478,2481)
1970: a(27) <123> 999 (56,58)
1971: a(27) <125> 999 (56,58)
1972: a(27) <128> 999 (56,58)
1973: a(28) <323> 999 (212,214)
1974: a(28) <377> 999 (212,214)
1975: a(24) <123> 999 (56,58)
1976: a(24) <125> 999 (56,58)
1977: a(24) <128> 999 (56,58)
1978: a(33) <1335> 999 (696,698), (900,902)
1979: a(33) <1417> 999 (696,698)
1980: a(35) <2412> 999 (753,755)
1981: a(35) <2412> 999 (753,755)
1982: a(27) <314> 999 (145,147)
1983: a(28) <549> 999 (470,472)
1984: a(27) <451> 999 (391,393)
1985: a(28) <577> 999 (506,508)
1986: a(23) <165> 999 (156,158)
1987: a(23) <165> 999 (156,158)
1988: a(32) <1736> 999 (417,419), (1539,1541)
1989: a(32) <1681> 999 (417,419)
1991: a(27) <628> 999 (202,204)
1992: a(27) <628> 999 (202,204)
1993: a(27) <628> 999 (202,204)
1994: a(27) <628> 999 (202,204)
1995: a(27) <628> 999 (202,204)
1996: a(27) <628> 999 (202,204)
1997: a(27) <628> 999 (202,204)
1998: a(27) <628> 999 (202,204)
1999: a(27) <628> 999 (202,204)
2496: a(36) <2412> 999 (753,755)
2497: a(36) <2412> 999 (753,755)
2498: a(36) <2412> 999 (753,755)
2499: a(36) <2412> 999 (753,755)
Each number is followed by the first a(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. Hopefully there's no mistakes.
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