Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #17 Jan 30 2021 10:49:06
%S 1,2,3,4,5,6,7,8,9,11,22,33,111,121,131,141,151,161,171,191,212,222,
%T 313,1111,1221,1331,2112,3113,11111,11211,11311,11411,11511,11711,
%U 12121,12221,13131,21112,21212,31113,111111,112211,121121
%N Palindromes in A083114.
%C Intersection of A117056 and A052382. - _Jayanta Basu_, May 15 2013
%H Charles R Greathouse IV and Chai Wah Wu, <a href="/A083115/b083115.txt">Table of n, a(n) for n = 1..2002</a> (n = 1..59 from Charles R Greathouse IV)
%F a(n) >> 3^n. - _Charles R Greathouse IV_, May 15 2013
%t id[n_]:=IntegerDigits[n]; palQ[n_]:=Reverse[x=id[n]]==x; t={}; Do[If[palQ[n] && (y=Times@@id[n])>0 && palQ[Plus@@id[n]] && palQ[y],AppendTo[t,n]],{n,125000}]; t (* _Jayanta Basu_, May 15 2013 *)
%t spQ[n_]:=Module[{idn=IntegerDigits[n]},FreeQ[idn,0]&&AllTrue[ {n,Total[ idn],Times@@idn},PalindromeQ]]; Select[Range[125000],spQ] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jan 30 2021 *)
%o (PARI) ispal(n)=n=digits(n);for(i=1,#n\2,if(n[i]!=n[#n+1-i],return(0)));1
%o is(n)=my(d=vecsort(digits(n)));d[1]&&ispal(sum(i=1,#d,d[i]))&&ispal(prod(i=1,#d,d[i]))&&ispal(n) \\ _Charles R Greathouse IV_, May 15 2013
%Y Cf. A083114.
%K base,nonn
%O 1,2
%A _Amarnath Murthy_, Apr 23 2003