A016885 a(n) = 5*n + 3.

3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, 63, 68, 73, 78, 83, 88, 93, 98, 103, 108, 113, 118, 123, 128, 133, 138, 143, 148, 153, 158, 163, 168, 173, 178, 183, 188, 193, 198, 203, 208, 213, 218, 223, 228, 233, 238, 243, 248, 253, 258, 263, 268, 273, 278, 283

Offset

0,1

Comments

Numbers ending in 3 or 8. - Lekraj Beedassy, Jul 08 2006

Number of moves in game of Brussels Sprouts with n+1 crosses. - Charles R Greathouse IV, Mar 09 2014

References

Elwyn R. Berlekamp, John Conway, and Richard K. Guy, Winning Ways for your Mathematical Plays, A K Peters, 2001.

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

Teena Gerhardt and Brady Haran, Brussels Sprouts, Numberphile video (2014).

Lancelot Hogben, Choice and Chance by Cardpack and Chessboard, Vol. 1, Max Parrish and Co, London, 1950, p. 36.

Tanya Khovanova, Recursive Sequences.

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

a(n) = floor((15*n+10)/3). - Gary Detlefs, Mar 07 2010

G.f.: (3+2*x)/(1-x)^2. - Colin Barker, Jan 08 2012

E.g.f.: (3 + 5*x)*exp(x). - G. C. Greubel, Jul 05 2019

a(n) = 2*a(n-1)-a(n-2). - Wesley Ivan Hurt, Apr 22 2021

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

a(n)^2 + (a(n)+1)^2 - n^2 = A017041(n)^2. - Charlie Marion, Apr 30 2023

Mathematica

Range[3, 300, 5] (* Vladimir Joseph Stephan Orlovsky, May 26 2011 *)

Prog

(PARI) a(n)=5*n+3 \\ Charles R Greathouse IV, Mar 09 2014
(Magma) [5*n+3: n in [0..60]]; // G. C. Greubel, Jul 05 2019
(GAP) List([0..60], n-> 5*n+3) # G. C. Greubel, Jul 05 2019

Crossrefs

Cf. A001622, A008587, A016861, A016873.

Cf. similar sequences with closed form (2*k-1)*n+k listed in A269044.

Sequence in context: A310306 A095762 A277600 * A190517 A105502 A105702

Adjacent sequences: A016882 A016883 A016884 * A016886 A016887 A016888

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from James A. Sellers, Jul 06 2000

Status

approved