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A221286 Vsemirnov's sequence. 8

%I #42 Dec 23 2023 08:44:01

%S 106276436867,35256392432,141532829299,176789221731,318322051030,

%T 495111272761,813433323791,1308544596552,2121977920343,3430522516895,

%U 5552500437238,8983022954133,14535523391371,23518546345504,38054069736875,61572616082379,99626685819254,161199301901633,260825987720887,422025289622520

%N Vsemirnov's sequence.

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

%H Seiichi Manyama, <a href="/A221286/b221286.txt">Table of n, a(n) for n = 0..4733</a> (terms 0..1000 from Alois P. Heinz)

%H Arturas Dubickas, Aivaras Novikas, and Jonas Šiurys, <a href="http://dx.doi.org/10.1016/j.jnt.2010.03.015">A binary linear recurrence sequence of composite numbers</a>, Journal of Number Theory, Volume 130, Issue 8, August 2010, Pages 1737-1749.

%H D. Ismailescu and J. Son, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Ismailescu/ism8.html">A New Kind of Fibonacci-Like Sequence of Composite Numbers</a>, J. Int. Seq. 17 (2014) # 14.8.2.

%H Maxim Vsemirnov, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL7/Vsemirnov/vsem5.html">A new Fibonacci-like sequence of composite numbers</a>, Journal of Integer Sequences 7:3 (2004).

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,1).

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

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

%p a:= n-> (<<0|1>, <1|1>>^n. <<106276436867, 35256392432>>)[1, 1]:

%p seq(a(n), n=0..20); # _Alois P. Heinz_, Apr 04 2013

%t LinearRecurrence[{1, 1}, {106276436867, 35256392432}, 20] (* _Alonso del Arte_, Feb 05 2013 *)

%o (PARI) Vec((106276436867-71020044435*x)/(1-x-x^2)+O(x^30)) \\ _Charles R Greathouse IV_, Dec 09 2014

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

%K nonn,easy

%O 0,1

%A _Charles R Greathouse IV_, Feb 05 2013

%E Offset corrected by _Alois P. Heinz_, Apr 04 2013

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)