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A082207
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Palindromes whose product of digits is a positive palindrome.
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2
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1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 111, 121, 131, 141, 151, 161, 171, 181, 191, 212, 222, 313, 676, 777, 1111, 1221, 1331, 2112, 3113, 11111, 11211, 11311, 11411, 11511, 11611, 11711, 11811, 11911, 12121, 12221, 13131, 16761, 17771, 21112, 21212
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OFFSET
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1,2
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COMMENTS
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The unary sequence A000042 is a trivial subsequence.
Conjecture: There are infinitely many terms in the sequence (of the type 777) for which the product of digits > 10.
Subset of A117055, containing terms for which product of digits is greater than 0. - Jayanta Basu, May 15 2013
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LINKS
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EXAMPLE
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777 is a term as 7^3 = 343 is a palindrome.
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MATHEMATICA
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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 *)
Select[Range[22000], FreeQ[IntegerDigits[#], 0]&&AllTrue[{#, Times @@ IntegerDigits[ #]}, PalindromeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 22 2019 *)
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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EXTENSIONS
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More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 19 2003
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STATUS
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approved
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