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%I #73 Jun 18 2023 18:31:42
%S 3,8,13,18,23,28,33,38,43,48,53,58,63,68,73,78,83,88,93,98,103,108,
%T 113,118,123,128,133,138,143,148,153,158,163,168,173,178,183,188,193,
%U 198,203,208,213,218,223,228,233,238,243,248,253,258,263,268,273,278,283
%N a(n) = 5*n + 3.
%C Numbers ending in 3 or 8. - _Lekraj Beedassy_, Jul 08 2006
%C Number of moves in game of Brussels Sprouts with n+1 crosses. - _Charles R Greathouse IV_, Mar 09 2014
%D Elwyn R. Berlekamp, John Conway, and Richard K. Guy, Winning Ways for your Mathematical Plays, A K Peters, 2001.
%H G. C. Greubel, <a href="/A016885/b016885.txt">Table of n, a(n) for n = 0..5000</a>
%H Teena Gerhardt and Brady Haran, <a href="https://www.youtube.com/watch?v=OAss481FfAQ">Brussels Sprouts</a>, Numberphile video (2014).
%H Lancelot Hogben, <a href="https://archive.org/details/chanceandchoiceb029729mbp/page/n39">Choice and Chance by Cardpack and Chessboard</a>, Vol. 1, Max Parrish and Co, London, 1950, p. 36.
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F a(n) = floor((15*n+10)/3). - _Gary Detlefs_, Mar 07 2010
%F G.f.: (3+2*x)/(1-x)^2. - _Colin Barker_, Jan 08 2012
%F E.g.f.: (3 + 5*x)*exp(x). - _G. C. Greubel_, Jul 05 2019
%F a(n) = 2*a(n-1)-a(n-2). - _Wesley Ivan Hurt_, Apr 22 2021
%F Sum_{n>=0} (-1)^n/a(n) = sqrt(2-2/sqrt(5))*Pi/10 - log(phi)/sqrt(5) + log(2)/5, where phi is the golden ratio (A001622). - _Amiram Eldar_, Apr 15 2023
%F a(n)^2 + (a(n)+1)^2 - n^2 = A017041(n)^2. - _Charlie Marion_, Apr 30 2023
%t Range[3, 300, 5] (* _Vladimir Joseph Stephan Orlovsky_, May 26 2011 *)
%o (PARI) a(n)=5*n+3 \\ _Charles R Greathouse IV_, Mar 09 2014
%o (Magma) [5*n+3: n in [0..60]]; // _G. C. Greubel_, Jul 05 2019
%o (GAP) List([0..60], n-> 5*n+3) # _G. C. Greubel_, Jul 05 2019
%Y Cf. A001622, A008587, A016861, A016873.
%Y Cf. similar sequences with closed form (2*k-1)*n+k listed in A269044.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
%E More terms from _James A. Sellers_, Jul 06 2000
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