A008589 Multiples of 7.

0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140, 147, 154, 161, 168, 175, 182, 189, 196, 203, 210, 217, 224, 231, 238, 245, 252, 259, 266, 273, 280, 287, 294, 301, 308, 315, 322, 329, 336, 343, 350, 357, 364, 371, 378

Offset: 0

Author

N. J. A. Sloane, Mar 15 1996

Keywords

• nonn
• easy

Comments

Also the Engel expansion of exp(1/7); cf. A006784 for the Engel expansion definition. - Benoit Cloitre, Mar 03 2002

Complement of A047304; A082784(a(n))=1; A109720(a(n))=0. - Reinhard Zumkeller, Nov 30 2009

The most likely sum of digits to occur when randomly tossing n pairs of (fair) six-sided dice. - Dennis P. Walsh, Jan 26 2012

Examples

			For n=2, a(2)=14 because 14 is the most likely sum (of the possible sums 4, 5, ..., 24) to occur when tossing 2 pairs of six-sided dice. - _Dennis P. Walsh_, Jan 26 2012
		

Links

• Ivan Panchenko, Table of n, a(n) for n = 0..200
• Edward Brooks, Divisibility by Seven, The Analyst, Vol. 2, No. 5 (Sep., 1875), pp. 129-131.
• Tanya Khovanova, Recursive Sequences
• Michael Penn, The Luckiest Divisibility Test, YouTube video, 2022.
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 319
• Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A008587, A008588, A016993.

Programs

Haskell

a008589 = (* 7)
a008589_list = [0, 7 ..]  -- Reinhard Zumkeller, Jan 25 2013

Magma

[7*n : n in [0..50]]; // Wesley Ivan Hurt, Jun 06 2014

Maple

A008589:=n->7*n; seq(A008589(n), n=0..50); # Wesley Ivan Hurt, Jun 06 2014

Mathematica

Range[0, 1000, 7] (* Vladimir Joseph Stephan Orlovsky, May 27 2011 *)
7*Range[0,60] (* Harvey P. Dale, Feb 28 2023 *)

Maxima

makelist(7*n,n,0,20); /* Martin Ettl, Dec 17 2012 */

PARI

a(n)=7*n \\ Charles R Greathouse IV, Jul 10 2016

Formula

(floor(a(n)/10) - 2*(a(n) mod 10)) == 0 modulo 7, see A076309. - Reinhard Zumkeller, Oct 06 2002

a(n) = 7*n = 2*a(n-1)-a(n-2); G.f.: 7*x/(x-1)^2. - Vincenzo Librandi, Dec 24 2010

E.g.f.: 7*x*exp(x). - Ilya Gutkovskiy, May 11 2016