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A241096 Palindromes in base 16 whose squares are also palindromes.

%I A241096 #29 Jun 09 2022 19:37:27
%S A241096 1,2,3,11,22,101,111,121,131,202,212,222,1001,1111,1221,2002,2112,
%T A241096 10001,10101,10201,10301,11011,11111,11211,11311,12021,12121,12221,
%U A241096 20002,20102,20202,21012,21112,21212,100001,101101,102201,110011,111111,112211,120021
%N A241096 Palindromes in base 16 whose squares are also palindromes.
%H A241096 Lars Blomberg, <a href="/A241096/b241096.txt">Table of n, a(n) for n = 1..10000</a>
%e A241096 131 is a term of this sequence because (unlike in base 10, where squaring 131 carries a 1 into the thousands place so that 131^2 is the non-palindromic number 17161) in base 16, 131^2 is 16B61.
%e A241096 141 is not a term because, even in base 16, a 1 is carried into the next place, so the result (19281) is not palindromic.
%o A241096 (Sage)
%o A241096 L=[]
%o A241096 for x in [1..100000]:
%o A241096     M=x.digits(base=16)
%o A241096     N=M[::-1]
%o A241096     if N == M:
%o A241096         d=x^2
%o A241096         D=d.digits(base=16)
%o A241096         E=D[::-1]
%o A241096         if D == E:
%o A241096             MM=(str(x) for x in M)
%o A241096             L.append(Integer(''.join(MM)))
%o A241096 L # _Tom Edgar_, Apr 29 2014
%Y A241096 Cf. A057135.
%K A241096 nonn,base
%O A241096 1,2
%A A241096 _J. Lowell_, Apr 26 2014
%E A241096 a(35)-a(41) from _Lars Blomberg_, Oct 23 2014