login
A088278
Smallest palindromic triangular numbers beginning with palindromes whose first digit is 1, 3, 5, 6, or 8.
0
1, 3, 55, 6, 8778, 114401848104411, 0, 55, 66, 0, 10129457886113466431168875492101, 11121736463712111
OFFSET
1,2
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.
EXAMPLE
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
Sequence in context: A193256 A319038 A340214 * A242199 A268661 A041155
KEYWORD
base,hard,more,nonn
AUTHOR
Amarnath Murthy, Sep 29 2003
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
STATUS
approved