A135639 a(n) = 839*n.

0, 839, 1678, 2517, 3356, 4195, 5034, 5873, 6712, 7551, 8390, 9229, 10068, 10907, 11746, 12585, 13424, 14263, 15102, 15941, 16780, 17619, 18458, 19297, 20136, 20975, 21814, 22653, 23492, 24331, 25170, 26009, 26848, 27687, 28526

Offset: 0

Author

Omar E. Pol, Nov 27 2007

Keywords

• easy
• nonn

Comments

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.

Examples

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

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• American Institute of Mathematics, Mathematicians Maps E_8.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

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

Programs

Mathematica

839Range[0,40] (* Harvey P. Dale, Sep 13 2011 *)
LinearRecurrence[{2,-1},{0,839},25] (* G. C. Greubel, Oct 25 2016 *)

Formula

From G. C. Greubel, Oct 25 2016: (Start)

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

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

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