A117055 Palindromes for which the product of the digits is also a palindrome.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 202, 212, 222, 303, 313, 404, 505, 606, 676, 707, 777, 808, 909, 1001, 1111, 1221, 1331, 2002, 2112, 3003, 3113, 4004, 5005, 6006, 7007, 8008, 9009, 10001, 10101

Offset

1,3

Links

Table of n, a(n) for n=1..52.

Example

676 is in the sequence because it is a palindrome and the product of its digits 6*7*6=252 is also a palindrome.

Mathematica

id[n_]:=IntegerDigits[n]; palQ[n_]:=Reverse[x=id[n]]==x; t={}; Do[If[palQ[n] && palQ[Times@@id[n]], AppendTo[t, n]], {n, 0, 10110}]; t (* Jayanta Basu, May 15 2013 *)

Prog

(PARI) isok(n) = my(d = digits(n), dp = digits(vecprod(d))); (Vecrev(d) == d) && (Vecrev(dp) == dp); \\ Michel Marcus, Nov 11 2019
(Magma) f:=func<n| Intseq(n) eq Reverse(Intseq(n))>; [k:k in [0..10000]| f(k) and f(&*Intseq(k))]; // Marius A. Burtea, Nov 11 2019

Crossrefs

Cf. A002113, A112875.

Sequence in context: A201061 A099165 A239480 * A117056 A082207 A083115

Adjacent sequences: A117052 A117053 A117054 * A117056 A117057 A117058

Keyword

nonn,base

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 16 2006

Status

approved