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A039685 Numbers m such that m^2 ends in 444. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

REFERENCES

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.

LINKS

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]

FORMULA

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)

MATHEMATICA

Drop[ Flatten[ Table[{500n-38, 500n+38}, {n, 0, 21}]], 1] (* Robert G. Wilson v, Nov 27 2004 *)

CROSSREFS

Cf. A328886 (squares that end in 444).

Sequence in context: A267474 A240258 A254471 * A006418 A160317 A088891

Adjacent sequences:  A039682 A039683 A039684 * A039686 A039687 A039688

KEYWORD

nonn,base

AUTHOR

Felice Russo

EXTENSIONS

More terms from Patrick De Geest, Jun 15 1999

STATUS

approved

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Last modified December 2 16:46 EST 2020. Contains 338877 sequences. (Running on oeis4.)