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A028553 Numbers k such that k*(k+3) is a palindrome.

%I A028553 #26 Oct 03 2023 17:08:28
%S A028553 0,1,8,28,66,88,211,298,671,2126,2998,28814,29369,29998,63701,212206,
%T A028553 212671,299998,636776,2122206,2861419,2999998,9443423,21341691,
%U A028553 28862883,29999998,212325206,289053683,294127328,294174669,299999998,2134473706,2946920844,2999999998
%N A028553 Numbers k such that k*(k+3) is a palindrome.
%C A028553 Also: numbers k such that the sum of the first k even composites is palindromic. Sequence is 4 + 6 + 8 + 10 + 12 + 14 + ... + z. For values of z see A058851. (Comment added by author 12/2000.)
%C A028553 All numbers of the form 3*10^j - 2 for j >= 0 are terms. For n > 1, a(n) mod 10 is one of {1,3,4,6,8,9}. - _Chai Wah Wu_, Feb 20 2021
%H A028553 Chai Wah Wu, <a href="/A028553/b028553.txt">Table of n, a(n) for n = 1..40</a>
%H A028553 Patrick De Geest, <a href="http://www.worldofnumbers.com/consemor.htm">Palindromic Quasipronics</a>
%H A028553 Patrick De Geest, <a href="http://www.worldofnumbers.com/firstpal.htm#sfn5">Palindromic Sums 2</a>
%H A028553 Erich Friedman, <a href="https://erich-friedman.github.io/numbers.html">What's Special About This Number?</a> (See entries 298, 2126, 2998.)
%t A028553 (Sqrt[4#+9]-3)/2&/@Select[Table[k(k+3),{k,0,3*10^6}],PalindromeQ] (* The program generates the first 22 terms of the sequence. *) (* _Harvey P. Dale_, Oct 03 2023 *)
%o A028553 (Python)
%o A028553 n, m, A028553_list = 0, 0, []
%o A028553 while n < 10**12:
%o A028553     s = str(m)
%o A028553     if s == s[::-1]:
%o A028553         A028553_list.append(n)
%o A028553     m += 2*(n+2)
%o A028553     n += 1 # _Chai Wah Wu_, Feb 20 2021
%Y A028553 Cf. A058852, A028554.
%K A028553 nonn,base
%O A028553 1,3
%A A028553 _Patrick De Geest_
%E A028553 More terms from _Chai Wah Wu_, Feb 20 2021