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A156674 Numbers k such that k^2 - 2 == 0 (mod 49). 1

%I #15 Jul 03 2023 11:10:15

%S 10,39,59,88,108,137,157,186,206,235,255,284,304,333,353,382,402,431,

%T 451,480,500,529,549,578,598,627,647,676,696,725,745,774,794,823,843,

%U 872,892,921,941,970,990,1019,1039,1068,1088,1117,1137,1166,1186,1215

%N Numbers k such that k^2 - 2 == 0 (mod 49).

%H Vincenzo Librandi, <a href="/A156674/b156674.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, -1).

%F G.f.: (10*x^2 + 29*x + 10)/(x^3 - x^2 - x + 1). - _Alexander R. Povolotsky_, Feb 15 2009

%F From _R. J. Mathar_, Feb 19 2009: (Start)

%F a(n) = a(n-1) + a(n-2) - a(n-3) = 49*n/2 - 49/4 + 9*(-1)^n/4.

%F G.f.: x*(2x+5)*(5x+2)/((1+x)*(1-x)^2). (End)

%e 10^2 - 2 == 0 (mod 49);

%e 39^2 - 2 == 0 (mod 49);

%e 59^2 - 2 == 0 (mod 49);

%e 88^2 - 2 == 0 (mod 49).

%t With[{c = 7^2}, Select[Range[1500], Divisible[#^2 - 2, c]&]] (* _Vincenzo Librandi_, Apr 06 2013 *)

%o (Magma) [Floor(n/2)*49-10*(-1)^n: n in [1..50]]; // _Vincenzo Librandi_, Apr 06 2013

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Feb 13 2009

%E Edited by _N. J. A. Sloane_, Feb 14 2009

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)