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, 18945, 19457, 19969, 20481

Offset

0,2

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).

Formula

From Vincenzo Librandi, Feb 23 2012: (Start)

G.f.: (1+511*x)/(1-x)^2.

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

From Elmo R. Oliveira, Jun 06 2026: (Start)

E.g.f.: exp(x)*(512*x + 1).

a(n) = 8*A152691(n) + 1. (End)

Mathematica

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

Prog

(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
(PARI) for(n=0, 50, print1(512*n+1", ")); \\ Vincenzo Librandi, Feb 23 2012
(Haskell)
a076338 n = (+ 1) . (* 512)
a076338_list = [1, 513..]  -- Reinhard Zumkeller, Mar 08 2012

Crossrefs

Cf. A076339, A152691.

Sequence in context: A060947 A182108 A066697 * A237620 A111344 A230188

Adjacent sequences: A076335 A076336 A076337 * A076339 A076340 A076341

Keyword

nonn,easy

Author

Reinhard Zumkeller, Oct 07 2002

Status

approved