A076338 a(n) = 512*n + 1.

1, 513, 1025, 1537, 2049, 2561, 3073, 3585, 4097, 4609, 5121, 5633, 6145, 6657, 7169, 7681, 8193, 8705, 9217, 9729, 10241, 10753, 11265, 11777, 12289, 12801, 13313, 13825, 14337, 14849, 15361, 15873, 16385, 16897, 17409, 17921, 18433

Offset: 0

Author

Reinhard Zumkeller, Oct 07 2002

Keywords

• nonn
• easy

Comments

First prime is a(15) = 7681, see A076339.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Tanya Khovanova, Recursive Sequences
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A076339.

Programs

Haskell

a076338 n = (+ 1) . (* 512)
a076338_list = [1,513..]  -- Reinhard Zumkeller, Mar 08 2012

Magma

I:=[1, 513]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Feb 23 2012

Mathematica

LinearRecurrence[{2, -1}, {1, 513}, 50] (* Vincenzo Librandi, Feb 23 2012 *)

PARI

for(n=0, 50, print1(512*n+1", ")); \\ Vincenzo Librandi, Feb 23 2012

Formula

G.f.: (1+511*x)/(1-x)^2. - Vincenzo Librandi, Feb 23 2012

a(n) = 2*a(n-1)-a(n-2). - Vincenzo Librandi, Feb 23 2012