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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A001622, A008587, A016861, A016873.

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

Programs

GAP

List([0..60], n-> 5*n+3); # G. C. Greubel, Jul 05 2019

Magma

[5*n+3: n in [0..60]]; // G. C. Greubel, Jul 05 2019

Mathematica

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

PARI

a(n)=5*n+3 \\ Charles R Greathouse IV, Mar 09 2014

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

Extensions

More terms from James Sellers, Jul 06 2000