A117056 Palindromes for which both the sum of the digits and the product of the digits are also palindromes.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 101, 111, 121, 131, 141, 151, 161, 171, 191, 202, 212, 222, 303, 313, 404, 1001, 1111, 1221, 1331, 2002, 2112, 3003, 3113, 4004, 10001, 10101, 10201, 10301, 10401, 10501, 10601, 10701, 10901, 11011, 11111, 11211

Offset: 1

Author

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

Keywords

• base
• nonn

Examples

			11711 is in the sequence because (1) it is a palindrome, (2)the sum of its digits 1+1+7+1+1=11 is a palindrome and (3)the product of its digits 1*1*7*1*1=7 is also a palindrome.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002113.

Programs

Mathematica

id[n_]:=IntegerDigits[n]; palQ[n_]:=Reverse[x=id[n]]==x; t={}; Do[If[palQ[n] && palQ[Plus@@id[n]] && palQ[Times@@id[n]],AppendTo[t,n]],{n,0,11220}]; t (* Jayanta Basu, May 15 2013 *)
Select[Range[0,12000],AllTrue[{#,Total[IntegerDigits[#]],Times@@IntegerDigits[#]},PalindromeQ]&] (* Harvey P. Dale, Jul 05 2022 *)

PARI

ispal(n)=n=digits(n);for(i=1,#n\2,if(n[i]!=n[#n+1-i],return(0)));1
is(n)=my(d=vecsort(digits(n)));ispal(sum(i=1,#d,d[i]))&&ispal(prod(i=1,#d,d[i]))&&ispal(n) \\ Charles R Greathouse IV, May 15 2013