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

1,3

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A002113.

Sequence in context: A099165 A239480 A117055 * A082207 A083115 A266280

Adjacent sequences: A117053 A117054 A117055 * A117057 A117058 A117059

Keyword

base,nonn

Author

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

Status

approved