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%I #26 Jul 02 2017 11:34:35
%S 1010,1011,1021,1031,1041,1051,1061,1071,1081,1091,1101,1121,1131,
%T 1141,1151,1161,1171,1181,1191,1201,1211,1212,1231,1241,1251,1261,
%U 1271,1281,1291,1301,1311,1313,1321,1341,1351,1361,1371,1381,1391,1401,1411,1414,1421
%N Non-palindromic numbers whose decimal expansion is a concatenation of the form a_1 a_2 a_3 ... a_{k-1} a_k a_k a_{k-1} ... a_2 a_1 (k >= 1) or a_1 a_2 a_3 ... a_{k-1} a_k a_{k-1} ... a_2 a_1 (k >= 2) for positive integers a_1, ..., a_k. For i>1, a_i may have leading zeros.
%C Of course any number m can be written as m = a_1, but this trivial construction is excluded.
%C A palindromic number of four digits has the form abba, where a is in {1, 2, ..., 9} and b is in {0, 1, 2, ..., 9}. There are 9x10=90 possibilities. For example, 1551 or 2002, but not 3753. However, 3753 = 3(75)3 and 4646 = (46)(46) are terms of the present sequence. The 4-digit numbers in the present sequence therefore have the form ABA, where A is in {1, 2, ..., 9} and B is in {00, 01, 02, 03, ..., 99} \ {00, 11, 22, 33, ..., 99}; or CC, where C is in {10, 11, 12, ..., 99} \ {11, 22, 33, ..., 99}. In the first case there are 9x(100-10)=9x90=810 terms. In the second case, 90-9=81. Total: 810+81=891 4-digit non-palindromic terms.
%D M. Khoshnevisan, manuscript, March 2003.
%D M. Khoshnevisan, "Generalized Smarandache Palindrome", Mathematics Magazine, Aurora, Canada, 10/2003.
%D M. Khoshnevisan, Proposed problem 1062, The PME Journal, USA, Vol. 11, No. 9, p. 501, 2003.
%H Peter Kagey, <a href="/A082461/b082461.txt">Table of n, a(n) for n = 1..10000</a>
%H Charles Ashbacher, Lori Neirynck, <a href="http://www.gallup.unm.edu/~smarandache/GeneralizedPalindromes.htm">The Density of Generalized Smarandache Palindromes</a>.
%H Charles Ashbacher, Lori Neirynck, <a href="/A082461/a082461.pdf"> The Density of Generalized Smarandache Palindromes</a> [Cached copy, pdf file]
%e For example, 1235656312 is a term because we can group it as (12)(3)(56)(56)(3)(12), i.e. ABCCBA.
%e 1010 = (10)(10), 1011 = 1(01)1, 1021 = 1(02)1, etc.
%K nonn,base
%O 1,1
%A K. Ramsharan (ramsharan(AT)indiainfo.com), Apr 26 2003
%E Edited by _N. J. A. Sloane_, Jul 02 2017
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