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A039685
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Numbers m such that m^2 ends in 444.
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9
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38, 462, 538, 962, 1038, 1462, 1538, 1962, 2038, 2462, 2538, 2962, 3038, 3462, 3538, 3962, 4038, 4462, 4538, 4962, 5038, 5462, 5538, 5962, 6038, 6462, 6538, 6962, 7038, 7462, 7538, 7962, 8038, 8462, 8538, 8962, 9038, 9462, 9538, 9962, 10038, 10462
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OFFSET
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1,1
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COMMENTS
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No square can end in more than three 4's.
When a square ends in exactly three identical digits, these digits are necessarily 444. - Bernard Schott, Oct 31 2019
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REFERENCES
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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.
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)
David Wells, "Curious and Interesting Numbers", Revised Ed. Penguin Books, p. 152. ISBN 0-14-026149-4.
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LINKS
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Table of n, a(n) for n=1..42.
British Mathematical Olympiad, 1995 - Problem 1
Index entries for linear recurrences with constant coefficients, signature (1,1,-1). [From Bruno Berselli, Oct 27 2010]
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FORMULA
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a(2n+1) = 500n + 38 and a(2n+2) = 500n - 38.
From Bruno Berselli, Oct 27 2010: (Start)
a(n) = 250*n + 87*(-1)^n - 125.
G.f.: 2*x*(19 + 212*x + 19*x^2)/((1+x)*(1-x)^2).
a(n) - a(n-1) - a(n-2) + a(n-3) = 0 for n > 3. (End)
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MATHEMATICA
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Drop[ Flatten[ Table[{500n-38, 500n+38}, {n, 0, 21}]], 1] (* Robert G. Wilson v, Nov 27 2004 *)
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CROSSREFS
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Cf. A328886 (squares that end in 444).
Sequence in context: A267474 A240258 A254471 * A006418 A160317 A088891
Adjacent sequences: A039682 A039683 A039684 * A039686 A039687 A039688
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KEYWORD
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nonn,base
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AUTHOR
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Felice Russo
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EXTENSIONS
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More terms from Patrick De Geest, Jun 15 1999
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STATUS
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approved
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