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A028504 Palindromes of form k*(k+2); or palindromes 1 less than a square.

%I A028504 #22 May 10 2025 23:13:57
%S A028504 0,3,8,99,323,575,4224,5775,9999,36863,42024,999999,3055503,3640463,
%T A028504 5597955,8803088,32855823,99999999,360696063,422919224,9999999999,
%U A028504 30485858403,30536863503,32154945123,59080108095,86310801368,304816618403,999999999999,3490500050943
%N A028504 Palindromes of form k*(k+2); or palindromes 1 less than a square.
%C A028504 10^(2*m) - 1 for m > 0 are terms. - _Chai Wah Wu_, May 25 2017
%H A028504 Giovanni Resta, <a href="/A028504/b028504.txt">Table of n, a(n) for n = 1..53</a>
%H A028504 P. De Geest, <a href="https://www.worldofnumbers.com/quapron.htm">Palindromic quasipronic numbers of the form n(n+2)</a>
%F A028504 a(n) = A028503(n) * (A028503(n) + 2) = A070253(n)^2 - 1 = A070254(n) - 1. - _Giovanni Resta_, Aug 29 2018
%e A028504 4224 belongs to this sequence as 4225 = 65^2.
%t A028504 palQ[n_] := Block[{d = IntegerDigits[n]}, d == Reverse[d]]; Select[Range[10000]^2 - 1, palQ] (* _Giovanni Resta_, Aug 29 2018 *)
%t A028504 Select[Table[n(n+2),{n,0,19*10^5}],PalindromeQ] (* _Harvey P. Dale_, Oct 13 2024 *)
%o A028504 (ARIBAS) stop := 400000; m := 1; while m < stop do s := m*m - 1; if s = int_reverse(s) then write(s," "); end; inc(m); end;
%Y A028504 Cf. A005563, A028503, A002779, A070253, A070254.
%K A028504 nonn,base
%O A028504 1,2
%A A028504 _Patrick De Geest_
%E A028504 More terms from _Giovanni Resta_, Aug 28 2018