A082207 Palindromes whose product of digits is a positive palindrome.

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

Offset

1,2

Comments

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

Links

Harvey P. Dale, Table of n, a(n) for n = 1..89 (all terms up to 10 million)

Example

777 is a term as 7^3 = 343 is a palindrome.

Mathematica

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 *)

Crossrefs

Cf. A082208.

Sequence in context: A239480 A117055 A117056 * A083115 A266280 A250412

Adjacent sequences: A082204 A082205 A082206 * A082208 A082209 A082210

Keyword

base,easy,nonn

Author

Amarnath Murthy, Apr 10 2003

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 19 2003

Status

approved