A229549 Numbers k such that k*(sum of digits of k) is a palindrome.

0, 1, 2, 3, 11, 22, 42, 53, 56, 101, 111, 113, 121, 124, 182, 187, 202, 272, 353, 434, 515, 572, 616, 683, 739, 829, 888, 1001, 1111, 1357, 1507, 1508, 1624, 1717, 2002, 2074, 2852, 3049, 3146, 3185, 3326, 3342, 3687, 3747, 4058, 4066, 4391, 4719, 4724, 5038, 7579, 8569, 9391, 9471

Offset: 1

Author

Derek Orr, Sep 26 2013

Keywords

• nonn
• base

Examples

			829*(8+2+9) = 15751 (palindrome), so 829 is a term of this sequence.
		

Links

• Delbert L. Johnson, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A057147.

Programs

Mathematica

palQ[n_] := Block[{d = IntegerDigits@ n}, d == Reverse@ d]; Select[Range@ 10000, palQ[# Plus @@ IntegerDigits@ #] &] (* Michael De Vlieger, Apr 12 2015 *)
Select[Range[0,10000],PalindromeQ[# Total[IntegerDigits[#]]]&] (* Harvey P. Dale, Jun 30 2025 *)

PARI

ispal(n)=d=digits(n);d==Vecrev(d)
for(n=0,10^4,s=sumdigits(n);if(ispal(n*s),print1(n,", "))) \\ Derek Orr, Apr 10 2015

Python

def ispal(n):
    r = ''
    for i in str(n):
        r = i + r
    return n == int(r)
def DS(n):
    s = 0
    for i in str(n):
        s += int(i)
    return s
{print(n, end=', ') for n in range(10**4) if ispal(n*DS(n))}
## Simplified by Derek Orr, Apr 10 2015

Extensions

More terms from Derek Orr, Apr 10 2015