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
Peter Kagey, Table of n, a(n) for n = 1..10000
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
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