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

0, 3, 8, 99, 323, 575, 4224, 5775, 9999, 36863, 42024, 999999, 3055503, 3640463, 5597955, 8803088, 32855823, 99999999, 360696063, 422919224, 9999999999, 30485858403, 30536863503, 32154945123, 59080108095, 86310801368, 304816618403, 999999999999, 3490500050943

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base

Comments

10^(2*m) - 1 for m > 0 are terms. - Chai Wah Wu, May 25 2017

Examples

			4224 belongs to this sequence as 4225 = 65^2.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..53
• P. De Geest, Palindromic quasipronic numbers of the form n(n+2)

Crossrefs

Cf. A005563, A028503, A002779, A070253, A070254.

Programs

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;

Mathematica

palQ[n_] := Block[{d = IntegerDigits[n]}, d == Reverse[d]]; Select[Range[10000]^2 - 1, palQ] (* Giovanni Resta, Aug 29 2018 *)
Select[Table[n(n+2),{n,0,19*10^5}],PalindromeQ] (* Harvey P. Dale, Oct 13 2024 *)

Formula

a(n) = A028503(n) * (A028503(n) + 2) = A070253(n)^2 - 1 = A070254(n) - 1. - Giovanni Resta, Aug 29 2018

Extensions

More terms from Giovanni Resta, Aug 28 2018