|
%I #42 Jun 07 2023 00:08:09
%S 144,169,441,961,10404,10609,12544,12769,14884,40401,44521,48841,
%T 90601,96721,1004004,1006009,1022121,1024144,1026169,1042441,1044484,
%U 1062961,1212201,1214404,1216609,1236544,1238769,1256641,1258884,1442401
%N Squares k^2 such that reverse(k)^2 = reverse(k^2), excluding squares of palindromes.
%C Subsequence of A035090. - _M. F. Hasler_, Mar 22 2011
%D David Wells, The Penguin Dictionary of Curious and Interesting Numbers, pp. 124, 127 (Rev. ed. 1997).
%H Giovanni Resta, <a href="/A064021/b064021.txt">Table of n, a(n) for n = 1..10000</a> (first 750 terms from Harry J. Smith)
%F {n = A000290(k) such that A004086(A000290(k)) = A000290(A004086(k)) and k is not in A002113}. - _Jonathan Vos Post_, May 02 2011
%F a(n) = A140212(n)^2. - _Giovanni Resta_, Jun 22 2018
%e 1026169 is included because its square root, 1013, when reversed (i.e., 3101) and squared yields 9616201.
%e 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
%t 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 *)
%t Select[Range[1250]^2,!PalindromeQ[Sqrt[#]]&&IntegerReverse[#] == IntegerReverse[ Sqrt[#]]^2 &&Mod[#,10]!=0&] (* _Harvey P. Dale_, Jul 01 2022 *)
%o (PARI) Rev(x)= { local(d,r); r=0; while (x>0, d=x-10*(x\10); x\=10; r=r*10 + d); return(r) }
%o { 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
%Y Cf. A035124, A035123, A033294, A140212.
%K nonn,base,nice
%O 1,1
%A _Harvey P. Dale_, Sep 18 2001
|
