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

%I A229549 #28 Jun 30 2025 13:19:43
%S A229549 0,1,2,3,11,22,42,53,56,101,111,113,121,124,182,187,202,272,353,434,
%T A229549 515,572,616,683,739,829,888,1001,1111,1357,1507,1508,1624,1717,2002,
%U A229549 2074,2852,3049,3146,3185,3326,3342,3687,3747,4058,4066,4391,4719,4724,5038,7579,8569,9391,9471
%N A229549 Numbers k such that k*(sum of digits of k) is a palindrome.
%H A229549 Delbert L. Johnson, <a href="/A229549/b229549.txt">Table of n, a(n) for n = 1..20000</a>
%e A229549 829*(8+2+9) = 15751 (palindrome), so 829 is a term of this sequence.
%t A229549 palQ[n_] := Block[{d = IntegerDigits@ n}, d == Reverse@ d]; Select[Range@ 10000, palQ[# Plus @@ IntegerDigits@ #] &] (* _Michael De Vlieger_, Apr 12 2015 *)
%t A229549 Select[Range[0,10000],PalindromeQ[# Total[IntegerDigits[#]]]&] (* _Harvey P. Dale_, Jun 30 2025 *)
%o A229549 (Python)
%o A229549 def ispal(n):
%o A229549     r = ''
%o A229549     for i in str(n):
%o A229549         r = i + r
%o A229549     return n == int(r)
%o A229549 def DS(n):
%o A229549     s = 0
%o A229549     for i in str(n):
%o A229549         s += int(i)
%o A229549     return s
%o A229549 {print(n, end=', ') for n in range(10**4) if ispal(n*DS(n))}
%o A229549 ## Simplified by _Derek Orr_, Apr 10 2015
%o A229549 (PARI) ispal(n)=d=digits(n);d==Vecrev(d)
%o A229549 for(n=0,10^4,s=sumdigits(n);if(ispal(n*s),print1(n,", "))) \\ _Derek Orr_, Apr 10 2015
%Y A229549 Cf. A057147.
%K A229549 nonn,base
%O A229549 1,3
%A A229549 _Derek Orr_, Sep 26 2013
%E A229549 More terms from _Derek Orr_, Apr 10 2015