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A221286 Vsemirnov's sequence. 1
106276436867, 35256392432, 141532829299, 176789221731, 318322051030, 495111272761, 813433323791, 1308544596552, 2121977920343, 3430522516895, 5552500437238, 8983022954133, 14535523391371, 23518546345504, 38054069736875, 61572616082379, 99626685819254, 161199301901633, 260825987720887, 422025289622520 (list; graph; refs; listen; history; text; internal format)
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

Alois P. Heinz, Table of n, a(n) for n = 0..1000

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.

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: A164935 A168340 A104799 * 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

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Last modified December 7 07:15 EST 2016. Contains 278841 sequences.