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A165989 Numbers such that n^2 = 29 mod 1193. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 9 00:20 EST 2022. Contains 358698 sequences. (Running on oeis4.)