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

1,2

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)

Formula

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

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 *)

Prog

(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, ", ")))

Crossrefs

Cf. A027719, A027720, A070254, A028503.

Sequence in context: A066915 A339924 A333673 * A147673 A298345 A057507

Adjacent sequences: A070250 A070251 A070252 * A070254 A070255 A070256

Keyword

nonn,base

Author

Amarnath Murthy, May 06 2002

Extensions

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

Status

approved