[seqfan] Re: Concatenate the sums of the neighboring digits

[Neil Sloane]

Hans, Thank you for the 109 proofs of correctness.  I have revised A328975
accordingly.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com



On Sat, Nov 2, 2019 at 4:46 PM Hans Havermann <gladhobo at bell.net> wrote:

> 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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>