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A082461
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Generalized Smarandache palindromes which are not palindromes: a generalized Smarandache palindrome (GSP) is a number of the form a1a2...anan...a2a1 or a1a2...an-1anan-1...a2a1, where all a1, a2, ..., an are positive integers of various number of digits.
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0
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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
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OFFSET
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0,1
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COMMENTS
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A palindromic number of four digits has the concatenated form: abba, where a is in {1, 2, ..., 9} and b is in {0, 1, 2, ..., 9}. There are 9x10=90 palindromic numbers of four digits. For example, 1551, or 2002 are palindromic (and, of course, GSP too); yet 3753 is not palindromic but it is a GSP for 3753=3(75)3, i.e. of the form ABA; similarly 4646, for it can be organized as (46)(46), i.e. of the form CC. Therefore a SGP, different from a palindromic number, should have the concatenated forms: 1) ABA, where A is in {1, 2, ?, 9} and B is in {00, 01, 02, 03, ?, 99}-{00, 11, 22, 33, ?, 99}; 2) or CC, where C is in {10, 11, 12, ?, 99}-{11, 22, 33, ?, 99}. In the first case, one has 9x(100-10)=9x90=810. In the second case, one has 90-9=81. Total: 810+81=891 GSP numbers of four digits which are not palindromic.
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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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Table of n, a(n) for n=0..24.
Charles Ashbacher, Lori Neirynck, The Density of Generalized Smarandache Palindromes.
G. Gregory, Generalized Smarandache Palindromes.
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FORMULA
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GSP of four digits are concatenated numbers of the forms: A(BC)A, where A is in {1, 2, 3, ..., 9} and both B, C in {0, 1, 2, ..., 9} with B different from C; or (AB)(AB), where A is in {1, 2, 3, ..., 9} and B in {0, 1, 2, ..., 9}, with A different from B.
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EXAMPLE
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For example:
a) 1235656312 is a Generalized Smarandache Palindrome (GSP) because we can group it as (12)(3)(56)(56)(3)(12), i.e. ABCCBA.
b) Obviously, any palindromic number is a GSP number as well.
c) Of course, any integer can be consider a GSP because we may consider the entire number as equal to a1, which is smarandachely palindromic; say N=176293 is GSP because we may take a1 = 176293 and thus N=a1. But one disregards this trivial case.
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CROSSREFS
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Sequence in context: A139059 A123156 A163278 * A071998 A043640 A145808
Adjacent sequences: A082458 A082459 A082460 * A082462 A082463 A082464
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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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STATUS
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approved
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