A229805 - OEIS

%I #15 Apr 07 2015 00:12:15

%S 0,1,2,3,11,22,101,111,121,202,272,353,434,515,616,888,1001,1111,2002,

%T 10001,10101,10201,10901,11011,11111,11711,12521,13331,14141,20002,

%U 20702,21512,22322,23132,30503,31313,32123,40304,41114,50105,100001,101101,110011,111111,200002,888888

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

%C Palindromes in the sequence A229549.

%H Giovanni Resta, <a href="/A229805/b229805.txt">Table of n, a(n) for n = 1..1000</a>

%e 888*(8+8+8) = 21312 (another palindrome). So, 888 is a member of this sequence.

%t 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 (Python)

%o def pal(n):

%o ..r = ''

%o ..for i in str(n):

%o ....r = i + r

%o ..return r == str(n)

%o def DS(n):

%o ..s = 0

%o ..for i in str(n):

%o ....s += int(i)

%o ..return s

%o {print(n,end=', ') for n in range(10**6) if pal(n)*pal(n*DS(n))}

%o ## Simplified by _Derek Orr_, Apr 05 2015

%o (PARI) pal(n)=d=digits(n);Vecrev(d)==d

%o for(n=0,10^6,s=sumdigits(n);if(pal(n)*pal(n*s),print1(n,", "))) \\ _Derek Orr_, Apr 05 2015

%Y Cf. A229549, A007953.

%K nonn,easy,base

%O 1,3

%A _Derek Orr_, Sep 29 2013