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A229805 Palindromes m such that m*(sum of digits of m) is also a palindrome. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Palindromes in the sequence A229549.

LINKS

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

EXAMPLE

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

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 *)

PROG

(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

(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

CROSSREFS

Cf. A229549, A007953.

Sequence in context: A229804 A241096 A057135 * A104075 A339753 A236168

Adjacent sequences:  A229802 A229803 A229804 * A229806 A229807 A229808

KEYWORD

nonn,easy,base

AUTHOR

Derek Orr, Sep 29 2013

STATUS

approved

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Last modified October 26 11:10 EDT 2021. Contains 348267 sequences. (Running on oeis4.)