A017257 a(n) = 9*n + 8.

8, 17, 26, 35, 44, 53, 62, 71, 80, 89, 98, 107, 116, 125, 134, 143, 152, 161, 170, 179, 188, 197, 206, 215, 224, 233, 242, 251, 260, 269, 278, 287, 296, 305, 314, 323, 332, 341, 350, 359, 368, 377, 386, 395, 404, 413, 422, 431, 440, 449, 458, 467, 476, 485

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Digital root of any number in this sequence = 8. Any partial sum of digits of any number in this sequence also belongs to this sequence. - Artur Jasinski, Dec 16 2007

Subsequence of A224829: A224823(a(n)) = 0. - Reinhard Zumkeller, Jul 21 2013

Links

• Tanya Khovanova, Recursive Sequences.
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 970.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A013656, A010701, A008591.

Programs

Haskell

a017257 = (+ 8) . (* 9)
a017257_list = 8 : map (+ 9) a017257_list  -- Reinhard Zumkeller, Jul 21 2013

Maple

A017257:=n->9*n+8; seq(A017257(n), n=0..100); # Wesley Ivan Hurt, Nov 30 2013

Mathematica

Array[9*#+8&,100,0] (* Vladimir Joseph Stephan Orlovsky, Dec 14 2009 *)

PARI

a(n)=9*n+8 \\ Charles R Greathouse IV, Sep 28 2015

Formula

a(n-1)^2 - A013656(n) * A010701(n)^2 = 1. - Vincenzo Librandi, Nov 19 2010

From Colin Barker, Jan 24 2012: (Start)

a(0)=8, a(1)=17, a(n) = 2*a(n-1)-a(n-2).

G.f.: (8+x)/(1-x)^2. (End)

E.g.f.: exp(x)*(8 + 9*x). - Stefano Spezia, Dec 08 2024