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A117056
Palindromes for which both the sum of the digits and the product of the digits are also palindromes.
2
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
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
KEYWORD
base,nonn
AUTHOR
Luc Stevens (lms022(AT)yahoo.com), Apr 16 2006
STATUS
approved