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%I #74 Feb 28 2023 09:25:11
%S 0,7,14,21,28,35,42,49,56,63,70,77,84,91,98,105,112,119,126,133,140,
%T 147,154,161,168,175,182,189,196,203,210,217,224,231,238,245,252,259,
%U 266,273,280,287,294,301,308,315,322,329,336,343,350,357,364,371,378
%N Multiples of 7.
%C Also the Engel expansion of exp(1/7); cf. A006784 for the Engel expansion definition. - _Benoit Cloitre_, Mar 03 2002
%C Complement of A047304; A082784(a(n))=1; A109720(a(n))=0. - _Reinhard Zumkeller_, Nov 30 2009
%C The most likely sum of digits to occur when randomly tossing n pairs of (fair) six-sided dice. - _Dennis P. Walsh_, Jan 26 2012
%H Ivan Panchenko, <a href="/A008589/b008589.txt">Table of n, a(n) for n = 0..200</a>
%H Edward Brooks, <a href="http://www.jstor.org/stable/2635933">Divisibility by Seven</a>, The Analyst, Vol. 2, No. 5 (Sep., 1875), pp. 129-131.
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H Michael Penn, <a href="https://www.youtube.com/watch?v=rgpwt_Vlz1E">The Luckiest Divisibility Test</a>, YouTube video, 2022.
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=319">Encyclopedia of Combinatorial Structures 319</a>
%H Luis Manuel Rivera, <a href="http://arxiv.org/abs/1406.3081">Integer sequences and k-commuting permutations</a>, arXiv preprint arXiv:1406.3081 [math.CO], 2014.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F (floor(a(n)/10) - 2*(a(n) mod 10)) == 0 modulo 7, see A076309. - _Reinhard Zumkeller_, Oct 06 2002
%F a(n) = 7*n = 2*a(n-1)-a(n-2); G.f.: 7*x/(x-1)^2. - _Vincenzo Librandi_, Dec 24 2010
%F E.g.f.: 7*x*exp(x). - _Ilya Gutkovskiy_, May 11 2016
%e 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
%p A008589:=n->7*n; seq(A008589(n), n=0..50); # _Wesley Ivan Hurt_, Jun 06 2014
%t Range[0, 1000, 7] (* _Vladimir Joseph Stephan Orlovsky_, May 27 2011 *)
%t 7*Range[0,60] (* _Harvey P. Dale_, Feb 28 2023 *)
%o (Maxima) makelist(7*n,n,0,20); /* _Martin Ettl_, Dec 17 2012 */
%o (Haskell)
%o a008589 = (* 7)
%o a008589_list = [0, 7 ..] -- _Reinhard Zumkeller_, Jan 25 2013
%o (Magma) [7*n : n in [0..50]]; // _Wesley Ivan Hurt_, Jun 06 2014
%o (PARI) a(n)=7*n \\ _Charles R Greathouse IV_, Jul 10 2016
%Y Cf. A008587, A008588, A016993.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Mar 15 1996
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