A064021 Squares k^2 such that reverse(k)^2 = reverse(k^2), excluding squares of palindromes.

144, 169, 441, 961, 10404, 10609, 12544, 12769, 14884, 40401, 44521, 48841, 90601, 96721, 1004004, 1006009, 1022121, 1024144, 1026169, 1042441, 1044484, 1062961, 1212201, 1214404, 1216609, 1236544, 1238769, 1256641, 1258884, 1442401

Offset: 1

Author

Harvey P. Dale, Sep 18 2001

Keywords

• nonn
• base
• nice

Comments

Subsequence of A035090. - M. F. Hasler, Mar 22 2011

Examples

			1026169 is included because its square root, 1013, when reversed (i.e., 3101) and squared yields 9616201.
Squares < 10 and 121 = 11^2, 484 = 22^2, ... are not in the sequence, since they are the square of a palindrome. - _M. F. Hasler_, Mar 22 2011
		

References

• David Wells, The Penguin Dictionary of Curious and Interesting Numbers, pp. 124, 127 (Rev. ed. 1997).

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 750 terms from Harry J. Smith)

Crossrefs

Cf. A035124, A035123, A033294, A140212.

Programs

Mathematica

Cases[Range[2000]^2, k_ /; Mod[k, 10] != 0 && IntegerDigits[k] != Reverse[IntegerDigits[k]] && FromDigits[Reverse[IntegerDigits[Sqrt[k]]]]^2 == FromDigits[Reverse[IntegerDigits[k]]]] (* Jean-François Alcover, Mar 22 2011 *)
Select[Range[1250]^2,!PalindromeQ[Sqrt[#]]&&IntegerReverse[#] == IntegerReverse[ Sqrt[#]]^2 &&Mod[#,10]!=0&] (* Harvey P. Dale, Jul 01 2022 *)

PARI

Rev(x)= { local(d,r); r=0; while (x>0, d=x-10*(x\10); x\=10; r=r*10 + d); return(r) }
{ n=0; for (m=1, 10^9, if (m%10==0, next); x=m^2; r=Rev(x); if (r==x, next); if (r==Rev(m)^2, write("b064021.txt", n++, " ", x); if (n==750, break)) ) } \\ Harry J. Smith, Sep 06 2009

Formula

{n = A000290(k) such that A004086(A000290(k)) = A000290(A004086(k)) and k is not in A002113}. - Jonathan Vos Post, May 02 2011

a(n) = A140212(n)^2. - Giovanni Resta, Jun 22 2018