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

1,1

Comments

Subsequence of A035090. - 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)

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A035124, A035123, A033294, A140212.

Sequence in context: A034289 A062917 A035090 * A156316 A323614 A245214

Adjacent sequences: A064018 A064019 A064020 * A064022 A064023 A064024

Keyword

nonn,base,nice

Author

Harvey P. Dale, Sep 18 2001

Status

approved