A039686 - OEIS

%I #33 Apr 26 2017 04:38:50

%S 49,169,361,1225,1444,1681,3249,4225,4900,15625,16900,36100,42025,

%T 49729,64009,81225,93025,122500,144400,168100,225625,237169,324900,

%U 422500,490000,519841,819025,950625,970225,1024144,1442401,1562500

%N Squares which are the concatenation of two nonzero squares.

%C Intersection of A191933 and A000290; A193095(a(n))>0 and A010052(a(n))=1. - _Reinhard Zumkeller_, Jul 17 2011

%C Note that "leading zeros" are not allowed, e.g., 9025 = 95^2 is not in the sequence although it is the concatenation of 9 = 3^2 and 025 = 5^2. - _M. F. Hasler_, Jan 25 2016

%D D. Wells, Curious and interesting numbers, Penguin Books, p. 152.

%H Giovanni Resta, <a href="/A039686/b039686.txt">Table of n, a(n) for n = 1..3000</a> (first 1000 terms from David W. Wilson)

%F a(n) = A048375(n)^2. - _M. F. Hasler_, Jan 25 2016

%e 1225=35^2, 225=15^2, 1=1^2.

%t t = Table[n^2, {n, 750}]; f[j_, k_] := Block[{n = j*10^Floor[1 + Log10@ k] + k}, If[IntegerQ@ Sqrt@ n, n, 0]]; Take[ Union@ Flatten@ Table[ f[t[[j]], t[[k]]], {j, 250}, {k, 750}], {2, 33}] (* _Robert G. Wilson v_, Jul 18 2011 *)

%t squareQ[n_] := IntegerQ[Sqrt[n]]; okQ[n_] := MatchQ[IntegerDigits[n], {a__ /; squareQ[FromDigits[{a}]], b__ /; First[{b}] > 0 && squareQ[FromDigits[ {b}]]}]; Select[Range[2000]^2, okQ] (* _Jean-François Alcover_, Dec 13 2016 *)

%o (Haskell)

%o a039686 n = a039686_list !! (n-1)

%o a039686_list = filter ((== 1) . a010052) a191933_list

%o -- _Reinhard Zumkeller_, Jul 17 2011

%o (PARI) is_A039686(n)={my(p=10);until(n<=p*=10,issquare(n%p)&&issquare(n\p)&&n%p*10>=p&&issquare(n)&&return(n>10))} \\ We must check whether n is a square but in practice this will be sure a priori (cf below) so we put this test at the end. The same applies for "n>10". - _M. F. Hasler_, Jan 25 2016

%o (PARI) {for(m=4,999, is_A039686(m^2)&&print1(m^2,","))} \\ Here the final checks issquare(n) & n>10 in the above function are superfluous, but they will only be done in the ("few") positive cases. - _M. F. Hasler_, Jan 25 2016

%Y Cf. A048375.

%K nonn,base

%O 1,1

%A _Felice Russo_

%E More terms from _Patrick De Geest_, March 1999