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

0, 1, 2, 3, 11, 22, 101, 111, 121, 202, 272, 353, 434, 515, 616, 888, 1001, 1111, 2002, 10001, 10101, 10201, 10901, 11011, 11111, 11711, 12521, 13331, 14141, 20002, 20702, 21512, 22322, 23132, 30503, 31313, 32123, 40304, 41114, 50105, 100001, 101101, 110011, 111111, 200002, 888888

Offset: 1

Author

Derek Orr, Sep 29 2013

Keywords

• nonn
• easy
• base

Comments

Palindromes in the sequence A229549.

Examples

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

Links

• Giovanni Resta, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A229549, A007953.

Programs

Mathematica

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 *)

PARI

pal(n)=d=digits(n);Vecrev(d)==d
for(n=0,10^6,s=sumdigits(n);if(pal(n)*pal(n*s),print1(n,", "))) \\ Derek Orr, Apr 05 2015

Python

def pal(n):
  r = ''
  for i in str(n):
    r = i + r
  return r == str(n)
def DS(n):
  s = 0
  for i in str(n):
    s += int(i)
  return s
{print(n, end=', ') for n in range(10**6) if pal(n)*pal(n*DS(n))}
## Simplified by Derek Orr, Apr 05 2015