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A039685 Numbers n such that n^2 ends in 444. 1
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.

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.

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.

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

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 February 22 14:58 EST 2017. Contains 282487 sequences.