A070253 - OEIS

%I #27 Oct 13 2024 13:07:15

%S 1,2,3,10,18,24,65,76,100,192,205,1000,1748,1908,2366,2967,5732,10000,

%T 18992,20565,100000,174602,174748,179318,243064,293787,552102,1000000,

%U 1868288,2967033,9200157,10000000,22765896,31552660,93809717,100000000

%N Numbers k such that k^2 - 1 is a palindrome.

%C Every palindrome of the form h^2-1 is of the form m*(m+2) (easy to prove by replacing h by m+1). In fact this is equal to A028503 + 1. - _Patrick De Geest_, May 09 2002

%H Giovanni Resta, <a href="/A070253/b070253.txt">Table of n, a(n) for n = 1..53</a>

%H P. De Geest, <a href="https://www.worldofnumbers.com/quapron.htm">Palindromic quasipronic numbers of the form n(n+2)</a>

%F a(n) = A028503(n) + 1. - _Giovanni Resta_, Aug 29 2018

%t Do[ If[ a = IntegerDigits[n^2 - 1]; a == Reverse[a], Print[n]], {n, 1, 10^8/4}]

%t Select[Range[10^8],PalindromeQ[#^2-1]&] (* _Harvey P. Dale_, Oct 13 2024 *)

%o (PARI) intreverse(n)=local(d,rev); rev=0; while(n>0,d=divrem(n,10); n=d[1]; rev=10*rev+d[2]); rev

%o for(n=1,100000000,q=n*n-1; if(q==intreverse(q),print1(n,",")))

%Y Cf. A027719, A027720, A070254, A028503.

%K nonn,base

%O 1,2

%A _Amarnath Murthy_, May 06 2002

%E Edited by _Jason Earls_, _Klaus Brockhaus_ and _Robert G. Wilson v_, May 08 2002