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URL: https://oeis.org/A221286

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A221286
Vsemirnov's sequence.
8
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, and 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 and 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).
FORMULA
a(n) = a(n-1) + a(n-2).
G.f.: (106276436867-71020044435*x)/(1-x-x^2).
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
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Offset corrected by Alois P. Heinz, Apr 04 2013
STATUS
approved