cp's OEIS Frontend

A229805 Palindromes m such that m*(sum of digits of m) is also a palindrome.

%I A229805 #19 Mar 01 2025 17:44:13
%S A229805 0,1,2,3,11,22,101,111,121,202,272,353,434,515,616,888,1001,1111,2002,
%T A229805 10001,10101,10201,10901,11011,11111,11711,12521,13331,14141,20002,
%U A229805 20702,21512,22322,23132,30503,31313,32123,40304,41114,50105,100001,101101,110011,111111,200002,888888
%N A229805 Palindromes m such that m*(sum of digits of m) is also a palindrome.
%C A229805 Palindromes in the sequence A229549.
%H A229805 Giovanni Resta, <a href="/A229805/b229805.txt">Table of n, a(n) for n = 1..1000</a>
%e A229805 888*(8+8+8) = 21312 (another palindrome). So, 888 is a member of this sequence.
%t A229805 palQ[n_]:=Module[{idn=IntegerDigits[n],idn2},idn2=IntegerDigits[ n*Total[ idn]];idn==Reverse[idn]&&idn2==Reverse[idn2]]; Select[Range[ 0,33000], palQ] (* _Harvey P. Dale_, May 20 2014 *)
%o A229805 (Python)
%o A229805 def pal(n):
%o A229805   r = ''
%o A229805   for i in str(n):
%o A229805     r = i + r
%o A229805   return r == str(n)
%o A229805 def DS(n):
%o A229805   s = 0
%o A229805   for i in str(n):
%o A229805     s += int(i)
%o A229805   return s
%o A229805 {print(n, end=', ') for n in range(10**6) if pal(n)*pal(n*DS(n))}
%o A229805 ## Simplified by _Derek Orr_, Apr 05 2015
%o A229805 (PARI) pal(n)=d=digits(n);Vecrev(d)==d
%o A229805 for(n=0,10^6,s=sumdigits(n);if(pal(n)*pal(n*s),print1(n,", "))) \\ _Derek Orr_, Apr 05 2015
%Y A229805 Cf. A229549, A007953.
%K A229805 nonn,easy,base
%O A229805 1,3
%A A229805 _Derek Orr_, Sep 29 2013