OFFSET
1,1
COMMENTS
A positive integer m we call k-digit half-palindrome if there exist two bases 1<b<c such that m=[m_1 m_2...m_k]_b=[m_k m_(k-1)...m_1]_c, where m_i are digits in both of these bases with the condition m_1>0 and m_k>0 (see SeqFan Discussion list from Mar 03 2011, where we introduced "b,c-palindromes").
Robert Israel showed (see SeqFan Discussion list from the same day) that every number of the form [n+1,n,n]_(2*n+1)is 3-digit half-palindrome with b=2*n+1 and c=2*n+2. Thus the sequence is infinite.
On the other hand, every number of the form [k*n+m+1,0,k*n+m]_(4*k*n+4*m+1), where k>=1,m>=0, is 3-digit half-palindrome with b=4*k*n+4*m+1 and c=4*k*n+4*m+3.
EXAMPLE
Let m=22. We have 22=[2 1 1]_3 and 22=[1 1 2]_4. Thus 22, by the definition, is a 3-digit half-palindrome.
Let m=91. We have 91=[3 3 1]_5 and 91 =[1 3 3]_8. Thus 91 is a 3-digit half palindrome.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Vladimir Shevelev, May 29 2011
EXTENSIONS
Corrected by R. J. Mathar, Jul 02 2012
STATUS
approved