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A082461
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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.
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2
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1010, 1011, 1021, 1031, 1041, 1051, 1061, 1071, 1081, 1091, 1101, 1121, 1131, 1141, 1151, 1161, 1171, 1181, 1191, 1201, 1211, 1212, 1231, 1241, 1251, 1261, 1271, 1281, 1291, 1301, 1311, 1313, 1321, 1341, 1351, 1361, 1371, 1381, 1391, 1401, 1411, 1414, 1421
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OFFSET
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1,1
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COMMENTS
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Of course any number m can be written as m = a_1, but this trivial construction is excluded.
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.
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REFERENCES
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M. Khoshnevisan, manuscript, March 2003.
M. Khoshnevisan, "Generalized Smarandache Palindrome", Mathematics Magazine, Aurora, Canada, 10/2003.
M. Khoshnevisan, Proposed problem 1062, The PME Journal, USA, Vol. 11, No. 9, p. 501, 2003.
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LINKS
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EXAMPLE
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For example, 1235656312 is a term because we can group it as (12)(3)(56)(56)(3)(12), i.e. ABCCBA.
1010 = (10)(10), 1011 = 1(01)1, 1021 = 1(02)1, etc.
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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K. Ramsharan (ramsharan(AT)indiainfo.com), Apr 26 2003
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EXTENSIONS
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STATUS
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approved
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