A221286 Vsemirnov's sequence.

106276436867, 35256392432, 141532829299, 176789221731, 318322051030, 495111272761, 813433323791, 1308544596552, 2121977920343, 3430522516895, 5552500437238, 8983022954133, 14535523391371, 23518546345504, 38054069736875, 61572616082379, 99626685819254, 161199301901633, 260825987720887, 422025289622520

Offset

0,1

Comments

A primefree linear recurrence with no common factors. As of 2004 no such sequences with smaller starting terms were known.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..4733 (terms 0..1000 from Alois P. Heinz)

Arturas Dubickas, Aivaras Novikas, Jonas Šiurys, A binary linear recurrence sequence of composite numbers, Journal of Number Theory, Volume 130, Issue 8, August 2010, Pages 1737-1749.

D. Ismailescu, J. Son, A New Kind of Fibonacci-Like Sequence of Composite Numbers, J. Int. Seq. 17 (2014) # 14.8.2.

Maxim Vsemirnov, A new Fibonacci-like sequence of composite numbers, Journal of Integer Sequences 7:3 (2004).

Index entries for linear recurrences with constant coefficients, signature (1,1).

Formula

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

G.f.: (106276436867-71020044435*x)/(1-x-x^2).

a(n) = 1/10*(-355100222175*((1/2+1/2*sqrt(5))^(n+1)+(1/2-1/2*sqrt(5))^(n+1)) +283572918169*sqrt(5)*((1/2+1/2*sqrt(5))^(n+1) -(1/2-1/2*sqrt(5))^(n+1))). - Paolo P. Lava, Feb 15 2013

Maple

a:= n-> (<<0|1>, <1|1>>^n. <<106276436867, 35256392432>>)[1, 1]:
seq(a(n), n=0..20);  # Alois P. Heinz, Apr 04 2013

Mathematica

LinearRecurrence[{1, 1}, {106276436867, 35256392432}, 20] (* Alonso del Arte, Feb 05 2013 *)

Prog

(PARI) Vec((106276436867-71020044435*x)/(1-x-x^2)+O(x^30)) \\ Charles R Greathouse IV, Dec 09 2014

Crossrefs

Other primefree linear recurrences: A083104 (Graham 1964), A082411 (Nicol 1999), A083105 (Knuth 1990), A083216 (Wilf 1990).

Sequence in context: A168340 A104799 A344751 * A074337 A072143 A233495

Adjacent sequences: A221283 A221284 A221285 * A221287 A221288 A221289

Keyword

nonn,easy

Author

Charles R Greathouse IV, Feb 05 2013

Extensions

Offset corrected by Alois P. Heinz, Apr 04 2013

Status

approved