A070253 Numbers k such that k^2 - 1 is a palindrome.

1, 2, 3, 10, 18, 24, 65, 76, 100, 192, 205, 1000, 1748, 1908, 2366, 2967, 5732, 10000, 18992, 20565, 100000, 174602, 174748, 179318, 243064, 293787, 552102, 1000000, 1868288, 2967033, 9200157, 10000000, 22765896, 31552660, 93809717, 100000000

Offset: 1

Author

Amarnath Murthy, May 06 2002

Keywords

• nonn
• base

Comments

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

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. A027719, A027720, A070254, A028503.

Programs

Mathematica

Do[ If[ a = IntegerDigits[n^2 - 1]; a == Reverse[a], Print[n]], {n, 1, 10^8/4}]
Select[Range[10^8],PalindromeQ[#^2-1]&] (* Harvey P. Dale, Oct 13 2024 *)

PARI

intreverse(n)=local(d,rev); rev=0; while(n>0,d=divrem(n,10); n=d[1]; rev=10*rev+d[2]); rev
for(n=1,100000000,q=n*n-1; if(q==intreverse(q),print1(n,",")))

Formula

a(n) = A028503(n) + 1. - Giovanni Resta, Aug 29 2018

Extensions

Edited by Jason Earls, Klaus Brockhaus and Robert G. Wilson v, May 08 2002