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%I #23 Jul 23 2023 01:50:22
%S 1,2,3,4,5,6,7,8,9,11,22,33,111,121,131,141,151,161,171,181,191,212,
%T 222,313,676,777,1111,1221,1331,2112,3113,11111,11211,11311,11411,
%U 11511,11611,11711,11811,11911,12121,12221,13131,16761,17771,21112,21212
%N Palindromes whose product of digits is a positive palindrome.
%C The unary sequence A000042 is a trivial subsequence.
%C Conjecture: There are infinitely many terms in the sequence (of the type 777) for which the product of digits > 10.
%C Subset of A117055, containing terms for which product of digits is greater than 0. - _Jayanta Basu_, May 15 2013
%H Harvey P. Dale, <a href="/A082207/b082207.txt">Table of n, a(n) for n = 1..89</a> (all terms up to 10 million)
%e 777 is a term as 7^3 = 343 is a palindrome.
%t id[n_]:=IntegerDigits[n]; palQ[n_]:=Reverse[x=id[n]]==x; t={}; Do[If[palQ[n] && (y=Times@@id[n]) > 0 && palQ[y], AppendTo[t,n]], {n,21220}]; t (* _Jayanta Basu_, May 15 2013 *)
%t Select[Range[22000],FreeQ[IntegerDigits[#],0]&&AllTrue[{#,Times @@ IntegerDigits[ #]},PalindromeQ]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Nov 22 2019 *)
%Y Cf. A082208.
%K base,easy,nonn
%O 1,2
%A _Amarnath Murthy_, Apr 10 2003
%E More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 19 2003