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a(1) = 1; a(n) = smallest multiple of a(n-1) which is a palindromic triangular number.
1

%I #11 Aug 11 2024 14:41:34

%S 1,3,6,66,8778,6172882716

%N a(1) = 1; a(n) = smallest multiple of a(n-1) which is a palindromic triangular number.

%C a(7) must be larger than 5*10^41. - _Patrick De Geest_

%H P. De Geest, <a href="https://www.worldofnumbers.com/em_alltria.htm">List of palindromic triangulars</a>

%t smpt[n_]:=Module[{k=2},While[!PalindromeQ[k*n]||!OddQ[Sqrt[1+8*k*n]],k++];k*n]; NestList[smpt,1,5] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jan 01 2019 *)

%Y Cf. A069501.

%K nonn,base,hard

%O 0,2

%A _Amarnath Murthy_, Mar 30 2002

%E a(6) from _Patrick De Geest_, Jun 11 2003