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%I #39 Feb 26 2023 02:35:05
%S 7,18,32,43,57,68,82,93,107,118,132,143,157,168,182,193,207,218,232,
%T 243,257,268,282,293,307,318,332,343,357,368,382,393,407,418,432,443,
%U 457,468,482,493,507,518,532,543,557,568,582,593,607,618,632,643,657,668
%N Numbers congruent to {7, 18} mod 25.
%C Also, numbers k such that k^2 + 1 == 0 (mod 25).
%C Numbers of the form 25*k+7 or 25*k+18. Numbers b such that 25 is a base-b Euler pseudoprime. - _Karsten Meyer_, Jan 05 2011
%H Vincenzo Librandi, <a href="/A156619/b156619.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 a(n) = 2*a(n-1)-a(n-2)-3, if n is even, and a(n) = 2*a(n-1)-a(n-2)+3, if n is odd, with a(1)=7, a(2)=18.
%F From _R. J. Mathar_, Feb 19 2009: (Start)
%F a(n) = a(n-1)+a(n-2)-a(n-3).
%F a(n) = 25*n/2-25/4-3*(-1)^n/4.
%F G.f.: x*(7+11*x+7*x^2)/((1+x)*(1-x)^2). (End)
%F E.g.f.: 7 + ((50*x - 25)*exp(x) - 3*exp(-x))/4. - _David Lovler_, Sep 08 2022
%F Sum_{n>=1} (-1)^(n+1)/a(n) = tan(11*Pi/50)*Pi/25. - _Amiram Eldar_, Feb 26 2023
%t fQ[n_] := Mod[n^2 + 1, 25] == 0; Select[ Range@ 670, fQ]
%t Flatten[#+{7,18}&/@(25*Range[0,30])] (* _Harvey P. Dale_, Jan 24 2013 *)
%t Select[Range[1, 700], MemberQ[{7, 18}, Mod[#, 25]]&] (* _Vincenzo Librandi_, Apr 08 2013 *)
%o (Magma) [n: n in [1..700] | n mod 25 in [7, 18]]; // _Vincenzo Librandi_, Apr 08 2013
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Feb 11 2009
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