A008587 Multiples of 5: a(n) = 5 * n.

0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195, 200, 205, 210, 215, 220, 225, 230, 235, 240, 245, 250, 255, 260, 265, 270, 275

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

1/31 = 0.0322580645... = (1/2)^5 + (1/2)^10 + (1/2)^15 + ... - Gary W. Adamson, Mar 14 2009

Complement of A047201; A079998(a(n))=1; A011558(a(n))=0. - Reinhard Zumkeller, Nov 30 2009

The y-intercept of a line perpendicular to y=mx,where m is the slope a/b and in this case a=2 and b=1, is a^2 + b^2 or 5, the first value of the list given. The remaining value are multiples of the first number of the list. - Larry J Zimmermann, Aug 21 2010

References

• Alfred S. Posamentier, Math Charmers, Tantalizing Tidbits for the Mind, Prometheus Books, NY, 2003, page 85.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Tanya Khovanova, Recursive Sequences
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 317
• Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. index to numbers of the form n*(d*n+10-d)/2 in A140090.

Cf. A008706, A011558, A020714, A030308, A047201, A079998.

Programs

Magma

[5*n: n in [0..60]]; // Vincenzo Librandi, Jun 10 2013

Mathematica

Range[0, 500, 5] (* Vladimir Joseph Stephan Orlovsky, May 26 2011 *)
NestList[#+5&,0,60] (* Harvey P. Dale, Dec 18 2023 *)

Maxima

makelist(5*n,n,0,20); /* Martin Ettl, Dec 17 2012 */

PARI

a(n)=5*n \\ Charles R Greathouse IV, Mar 22 2016

Formula

From R. J. Mathar, May 26 2008: (Start)

O.g.f.: 5x/(1-x)^2.

a(n) = A008706(n), n > 0. (End)

a(n) = Sum_{k>=0} A030308(n,k)*A020714(k). - Philippe Deléham, Oct 17 2011

E.g.f.: 5*x*exp(x). - Stefano Spezia, Aug 19 2024