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A057136 Palindromes whose square root is a palindrome.

%I A057136 #23 Apr 26 2019 17:16:42
%S A057136 0,1,4,9,121,484,10201,12321,14641,40804,44944,1002001,1234321,
%T A057136 4008004,100020001,102030201,104060401,121242121,123454321,125686521,
%U A057136 400080004,404090404,10000200001,10221412201,12102420121,12345654321,40000800004
%N A057136 Palindromes whose square root is a palindrome.
%C A057136 Always contain an odd number of digits.
%H A057136 Robert Israel, <a href="/A057136/b057136.txt">Table of n, a(n) for n = 1..10000</a>  (n=1..412 from N. J. A. Sloane based on R. J. Mathar's b-file for A057135)
%F A057136 a(n) = A057135(n)^2
%e A057136 a(8) = 14641 since 14641 = 121^2 and 121 is also a palindrome
%p A057136 dmax:= 7: # to get all terms with up to dmax digits
%p A057136 Res:= 0,1,2^2,3^2,11^2,22^2:
%p A057136 Po:= [[0],[1],[2],[3]]: Pe:= [[0,0],[1,1],[2,2]]:
%p A057136 for d from 1 to dmax do
%p A057136   if d::odd then
%p A057136     Po:= select(t -> add(s^2,s=t) < 10, [seq(seq([i,op(t),i], t=Po),i=0..2)]);
%p A057136     Res:= Res, op(map(proc(p) if p[1] <> 0 then add(p[i]*10^(i-1),i=1..nops(p))^2 fi end proc, Po))
%p A057136   else
%p A057136     Pe:= select(t -> add(s^2,s=t) < 10, [seq(seq([i,op(t),i], t=Pe),i=0..2)]);
%p A057136     Res:= Res, op(map(proc(p) if p[1] <> 0 then add(p[i]*10^(i-1),i=1..nops(p))^2 fi end proc, Pe))
%p A057136   fi;
%p A057136 od:
%p A057136 Res; # _Robert Israel_, Jun 21 2017
%t A057136 Select[Range[0, 10^6], PalindromeQ[#] && PalindromeQ[#^2] &]^2 (* _Robert Price_, Apr 26 2019 *)
%Y A057136 Cf. A000290, A002113, A002779, A057135 (the square roots).
%K A057136 base,nonn
%O A057136 1,3
%A A057136 _Henry Bottomley_, Aug 12 2000