This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A039685 #41 Sep 15 2024 18:02:12
%S A039685 38,462,538,962,1038,1462,1538,1962,2038,2462,2538,2962,3038,3462,
%T A039685 3538,3962,4038,4462,4538,4962,5038,5462,5538,5962,6038,6462,6538,
%U A039685 6962,7038,7462,7538,7962,8038,8462,8538,8962,9038,9462,9538,9962,10038,10462
%N A039685 Numbers m such that m^2 ends in 444.
%C A039685 No square can end in more than three 4's.
%C A039685 When a square ends in exactly three identical digits, these digits are necessarily 444. - _Bernard Schott_, Oct 31 2019
%D A039685 Albert H. Beiler, "Recreations in the Theory of Numbers", Dover Publ., 2nd Ed. 1966, Chapter XV, "On The Square", p. 139. ISBN 0-486-21096-0.
%D A039685 A. Gardiner, The Mathematical Olympiad Handbook: An Introduction to Problem Solving, Oxford University Press, 1997, reprinted 2011, Pb 1 pp. 55 and 95-96 (1995)
%D A039685 David Wells, "Curious and Interesting Numbers", Revised Ed. Penguin Books, p. 152. ISBN 0-14-026149-4.
%H A039685 Harvey P. Dale, <a href="/A039685/b039685.txt">Table of n, a(n) for n = 1..1000</a>
%H A039685 British Mathematical Olympiad, <a href="https://bmos.ukmt.org.uk/home/bmo1-1995.pdf">1995 - Problem 1</a>.
%H A039685 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A039685 a(2n+1) = 500n + 38 and a(2n+2) = 500n - 38.
%F A039685 From _Bruno Berselli_, Oct 27 2010: (Start)
%F A039685 a(n) = 250*n + 87*(-1)^n - 125.
%F A039685 G.f.: 2*x*(19 + 212*x + 19*x^2)/((1+x)*(1-x)^2).
%F A039685 a(n) - a(n-1) - a(n-2) + a(n-3) = 0 for n > 3. (End)
%F A039685 E.g.f.: 38 + (250*x - 38)*cosh(x) + (250*x - 212)*sinh(x). - _Stefano Spezia_, Sep 15 2024
%t A039685 Drop[ Flatten[ Table[{500n-38, 500n+38}, {n, 0, 21}]], 1] (* _Robert G. Wilson v_, Nov 27 2004 *)
%t A039685 Sqrt[#]&/@Select[Range[15000]^2,Mod[#,1000]==444&] (* or *) LinearRecurrence[{1,1,-1},{38,462,538},50] (* _Harvey P. Dale_, Dec 26 2023 *)
%Y A039685 Cf. A328886 (squares that end in 444).
%K A039685 nonn,base,easy
%O A039685 1,1
%A A039685 _Felice Russo_
%E A039685 More terms from _Patrick De Geest_, Jun 15 1999