cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A117056 #11 Jul 05 2022 18:02:02
%S A117056 0,1,2,3,4,5,6,7,8,9,11,22,33,101,111,121,131,141,151,161,171,191,202,
%T A117056 212,222,303,313,404,1001,1111,1221,1331,2002,2112,3003,3113,4004,
%U A117056 10001,10101,10201,10301,10401,10501,10601,10701,10901,11011,11111,11211
%N A117056 Palindromes for which both the sum of the digits and the product of the digits are also palindromes.
%H A117056 Chai Wah Wu, <a href="/A117056/b117056.txt">Table of n, a(n) for n = 1..10000</a>
%e A117056 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.
%t A117056 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 *)
%t A117056 Select[Range[0,12000],AllTrue[{#,Total[IntegerDigits[#]],Times@@IntegerDigits[#]},PalindromeQ]&] (* _Harvey P. Dale_, Jul 05 2022 *)
%o A117056 (PARI) ispal(n)=n=digits(n);for(i=1,#n\2,if(n[i]!=n[#n+1-i],return(0)));1
%o A117056 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
%Y A117056 Cf. A002113.
%K A117056 base,nonn
%O A117056 1,3
%A A117056 Luc Stevens (lms022(AT)yahoo.com), Apr 16 2006