A088278 Smallest palindromic triangular numbers beginning with palindromes whose first digit is 1, 3, 5, 6, or 8.

1, 3, 55, 6, 8778, 114401848104411, 0, 55, 66, 0, 10129457886113466431168875492101, 11121736463712111

Offset: 1

Author

Amarnath Murthy, Sep 29 2003

Keywords

• base
• hard
• more
• nonn

Comments

The possible values of the ones digit of a triangular number are 0,1,3,5,6 and 8. Similarly, one can list the two-digit numbers k such that a triangular number of the form 100r + k can exist, and so on for the first three digits, etc. For palindromes P beginning with numbers other than these (e.g., for 33 and 88, which are two-digit palindromes P that start with 1, 3, 5, 6, or 8 but are not in A187127), the corresponding term is 0.

Examples

			From _Jon E. Schoenfield_, Mar 03 2018: (Start)
        Palindrome P       a(n) = smallest palindromic
       starting with    triangular number starting with P
   n  1, 3, 5, 6, or 8   (or 0 if no such number exists)
  ==  ================  =================================
   1          1                                         1
   2          3                                         3
   3          5                                        55
   4          6                                         6
   5          8                                      8778
   6         11                           114401848104411
   7         33                                         0
   8         55                                        55
   9         66                                        66
  10         88                                         0
  11        101          10129457886113466431168875492101
  12        111                         11121736463712111
  13        121                                         ?
  14        131                             1313207023131
  15        141                                         ?
  16        151                      15199896744769899151
  17        161                                         ?
  18        171                                       171
  19        181                                         ?
  20        191                                         ?
  21        303                                         0
(End)
		

Crossrefs

Cf. A003098 (palindromic triangular numbers), A187127 (numbers that are the residue mod 100 of a triangular number). - Jon E. Schoenfield, Mar 03 2018

Extensions

Name and Comments edited, offset changed to 1, and a(11) and a(12) corrected (a(11) taken from b-file at A003098) by Jon E. Schoenfield, Mar 03 2018