A135639 - OEIS

%I #22 Dec 11 2019 10:47:50

%S 0,839,1678,2517,3356,4195,5034,5873,6712,7551,8390,9229,10068,10907,

%T 11746,12585,13424,14263,15102,15941,16780,17619,18458,19297,20136,

%U 20975,21814,22653,23492,24331,25170,26009,26848,27687,28526

%N a(n) = 839*n.

%C The 146th prime number (839) and some of its multiples are related to the exceptional Lie group E_8 calculation because the result is a matrix with 453060 rows and columns. The size of the matrix is the member a(540)=453060 of this sequence. The number 839 is the largest prime factor of 453060 because we can write 2*2*3*3*3*5*839=453060. The number of entries of the matrix is the member a(244652400)=453060*453060=205263363600.

%H G. C. Greubel, <a href="/A135639/b135639.txt">Table of n, a(n) for n = 0..1000</a>

%H American Institute of Mathematics, <a href="http://aimath.org/E8">Mathematicians Maps E_8</a>.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F From _G. C. Greubel_, Oct 25 2016: (Start)

%F a(n) = 2*a(n-1) - a(n-2).

%F G.f.: (839*x)/(1 - x)^2.

%F E.g.f.: 839*x*exp(x). (End)

%e a(1)=839. a(540)=540*839=453060. a(244652400)=244652400*839=205263363600.

%t 839Range[0,40] (* _Harvey P. Dale_, Sep 13 2011 *)

%t LinearRecurrence[{2,-1},{0,839},25] (* _G. C. Greubel_, Oct 25 2016 *)

%Y Cf. A064730, A134888, A134950, A134960, A135631.

%K easy,nonn

%O 0,2

%A _Omar E. Pol_, Nov 27 2007