A165989 Numbers such that n^2 = 29 mod 1193.

534, 659, 1727, 1852, 2920, 3045, 4113, 4238, 5306, 5431, 6499, 6624, 7692, 7817, 8885, 9010, 10078, 10203, 11271, 11396, 12464, 12589, 13657, 13782, 14850, 14975, 16043, 16168, 17236, 17361, 18429, 18554, 19622, 19747, 20815, 20940, 22008, 22133, 23201

Offset

1,1

References

Albert H. Beiler, Recreations in the Theory of Numbers: The Queen of Mathematics Entertains at 203, 315 (2d ed. 1966)

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Formula

a(1) = 534, a(2) = 659, a(3) = 1727, a(n) = a(n-1) +a(n-2) -a(n-3). - Harvey P. Dale, Oct 22 2012

From Colin Barker, Aug 07 2013: (Start)

a(n) = (-1193 -943*(-1)^n +2386*n)/4.

G.f.: x*(534*x^2+125*x+534) / ((x-1)^2*(x+1)). (End)

E.g.f.: (943*exp(-x) + 1193*(1 + 2*x)*exp(x))/4. - Ilya Gutkovskiy, Apr 21 2016

Example

1727^2 = 2982529, and 2982529 divided by 1193 leaves a remainder of 29

Mathematica

Sqrt[ # ]&/@Select[Range[20000]^2, Mod[ #, 1193]==29&]
LinearRecurrence[{1, 1, -1}, {534, 659, 1727}, 40] (* Harvey P. Dale, Oct 22 2012 *)
Select[Range[25000], PowerMod[#, 2, 1193]==29&] (* Harvey P. Dale, Apr 29 2015 *)

Crossrefs

Sequence in context: A098258 A160176 A077085 * A183598 A252536 A067723

Adjacent sequences: A165986 A165987 A165988 * A165990 A165991 A165992

Keyword

easy,nonn

Author

Harvey P. Dale, Oct 03 2009

Extensions

More terms from Colin Barker, Aug 07 2013

Status

approved