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Squares that end in 444.
4

%I #16 Jan 26 2025 18:23:58

%S 1444,213444,289444,925444,1077444,2137444,2365444,3849444,4153444,

%T 6061444,6441444,8773444,9229444,11985444,12517444,15697444,16305444,

%U 19909444,20593444,24621444,25381444,29833444,30669444,35545444,36457444,41757444,42745444,48469444

%N Squares that end in 444.

%C See A039685 for further information about these numbers.

%H Harvey P. Dale, <a href="/A328886/b328886.txt">Table of n, a(n) for n = 1..400</a>

%H Albert H. Beiler, Recreations in the Theory of Numbers (2d ed. 1966), p.139.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).

%F a(n) = A039685(n)^2.

%t Select[Table[n*10^3+444,{n,50000}],IntegerQ[Sqrt[#]]&] (* _Harvey P. Dale_, Jun 19 2020 *)

%t Flatten[Table[500n+{38,-38},{n,0,20}]]^2//Union (* _Harvey P. Dale_, Jan 26 2025 *)

%o (PARI) a039685(n) = 250*n+87*(-1)^n-125

%o a(n) = a039685(n)^2

%Y Cf. A039685.

%K nonn,base,easy

%O 1,1

%A _Felix Fröhlich_, Oct 29 2019