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A082461
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.
2
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
OFFSET
1,1
COMMENTS
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.
REFERENCES
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.
LINKS
Charles Ashbacher, Lori Neirynck, The Density of Generalized Smarandache Palindromes.
Charles Ashbacher, Lori Neirynck, The Density of Generalized Smarandache Palindromes [Cached copy, pdf file]
EXAMPLE
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.
CROSSREFS
Sequence in context: A139059 A123156 A163278 * A071998 A043640 A286138
KEYWORD
nonn,base
AUTHOR
K. Ramsharan (ramsharan(AT)indiainfo.com), Apr 26 2003
EXTENSIONS
Edited by N. J. A. Sloane, Jul 02 2017
STATUS
approved