A191279 3-digit half-palindromes.

22, 51, 87, 91, 102, 121, 145, 169, 187, 190, 212, 220, 225, 245, 247, 248

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.

Links

Table of n, a(n) for n=1..16.

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

Cf. A002113, A006995, A059809

Sequence in context: A043948 A015226 A092221 * A200880 A330409 A111576

Adjacent sequences: A191276 A191277 A191278 * A191280 A191281 A191282

Keyword

nonn,base

Author

Vladimir Shevelev, May 29 2011

Extensions

Corrected by R. J. Mathar, Jul 02 2012

Status

approved