A057136 - OEIS

%I #23 Apr 26 2019 17:16:42

%S 0,1,4,9,121,484,10201,12321,14641,40804,44944,1002001,1234321,

%T 4008004,100020001,102030201,104060401,121242121,123454321,125686521,

%U 400080004,404090404,10000200001,10221412201,12102420121,12345654321,40000800004

%N Palindromes whose square root is a palindrome.

%C Always contain an odd number of digits.

%H 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 a(n) = A057135(n)^2

%e a(8) = 14641 since 14641 = 121^2 and 121 is also a palindrome

%p dmax:= 7: # to get all terms with up to dmax digits

%p Res:= 0,1,2^2,3^2,11^2,22^2:

%p Po:= [[0],[1],[2],[3]]: Pe:= [[0,0],[1,1],[2,2]]:

%p for d from 1 to dmax do

%p   if d::odd then

%p     Po:= select(t -> add(s^2,s=t) < 10, [seq(seq([i,op(t),i], t=Po),i=0..2)]);

%p     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   else

%p     Pe:= select(t -> add(s^2,s=t) < 10, [seq(seq([i,op(t),i], t=Pe),i=0..2)]);

%p     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   fi;

%p od:

%p Res; # _Robert Israel_, Jun 21 2017

%t Select[Range[0, 10^6], PalindromeQ[#] && PalindromeQ[#^2] &]^2 (* _Robert Price_, Apr 26 2019 *)

%Y Cf. A000290, A002113, A002779, A057135 (the square roots).

%K base,nonn

%O 1,3

%A _Henry Bottomley_, Aug 12 2000