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

%I A088278 #15 Mar 06 2018 11:27:47
%S A088278 1,3,55,6,8778,114401848104411,0,55,66,0,
%T A088278 10129457886113466431168875492101,11121736463712111
%N A088278 Smallest palindromic triangular numbers beginning with palindromes whose first digit is 1, 3, 5, 6, or 8.
%C A088278 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.
%e A088278 From _Jon E. Schoenfield_, Mar 03 2018: (Start)
%e A088278         Palindrome P       a(n) = smallest palindromic
%e A088278        starting with    triangular number starting with P
%e A088278    n  1, 3, 5, 6, or 8   (or 0 if no such number exists)
%e A088278   ==  ================  =================================
%e A088278    1          1                                         1
%e A088278    2          3                                         3
%e A088278    3          5                                        55
%e A088278    4          6                                         6
%e A088278    5          8                                      8778
%e A088278    6         11                           114401848104411
%e A088278    7         33                                         0
%e A088278    8         55                                        55
%e A088278    9         66                                        66
%e A088278   10         88                                         0
%e A088278   11        101          10129457886113466431168875492101
%e A088278   12        111                         11121736463712111
%e A088278   13        121                                         ?
%e A088278   14        131                             1313207023131
%e A088278   15        141                                         ?
%e A088278   16        151                      15199896744769899151
%e A088278   17        161                                         ?
%e A088278   18        171                                       171
%e A088278   19        181                                         ?
%e A088278   20        191                                         ?
%e A088278   21        303                                         0
%e A088278 (End)
%Y A088278 Cf. A003098 (palindromic triangular numbers), A187127 (numbers that are the residue mod 100 of a triangular number). - _Jon E. Schoenfield_, Mar 03 2018
%K A088278 base,hard,more,nonn
%O A088278 1,2
%A A088278 _Amarnath Murthy_, Sep 29 2003
%E A088278 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