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Smallest palindromic triangular numbers beginning with palindromes whose first digit is 1, 3, 5, 6, or 8.
0

%I #15 Mar 06 2018 11:27:47

%S 1,3,55,6,8778,114401848104411,0,55,66,0,

%T 10129457886113466431168875492101,11121736463712111

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

%C 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 From _Jon E. Schoenfield_, Mar 03 2018: (Start)

%e Palindrome P a(n) = smallest palindromic

%e starting with triangular number starting with P

%e n 1, 3, 5, 6, or 8 (or 0 if no such number exists)

%e == ================ =================================

%e 1 1 1

%e 2 3 3

%e 3 5 55

%e 4 6 6

%e 5 8 8778

%e 6 11 114401848104411

%e 7 33 0

%e 8 55 55

%e 9 66 66

%e 10 88 0

%e 11 101 10129457886113466431168875492101

%e 12 111 11121736463712111

%e 13 121 ?

%e 14 131 1313207023131

%e 15 141 ?

%e 16 151 15199896744769899151

%e 17 161 ?

%e 18 171 171

%e 19 181 ?

%e 20 191 ?

%e 21 303 0

%e (End)

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

%K base,hard,more,nonn

%O 1,2

%A _Amarnath Murthy_, Sep 29 2003

%E 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