This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A083105 #39 Feb 07 2025 22:47:41
%S A083105 62638280004239857,49463435743205655,112101715747445512,
%T A083105 161565151490651167,273666867238096679,435232018728747846,
%U A083105 708898885966844525,1144130904695592371,1853029790662436896,2997160695358029267,4850190486020466163,7847351181378495430
%N A083105 Second-order linear recurrence sequence with a(n) = a(n-1) + a(n-2), with initial terms 62638280004239857, 49463435743205655.
%C A083105 a(0) = 62638280004239857, a(1) = 49463435743205655. This is a second-order linear recurrence sequence with a(0) and a(1) coprime that does not contain any primes. It was found by D. E. Knuth in 1990.
%H A083105 Seiichi Manyama, <a href="/A083105/b083105.txt">Table of n, a(n) for n = 0..4705</a>
%H A083105 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 A083105 R. L. Graham, <a href="http://www.jstor.org/stable/2689243">A Fibonacci-Like sequence of composite numbers</a>, Math. Mag. 37 (1964) 322-324.
%H A083105 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 A083105 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A083105 D. E. Knuth, <a href="http://www.jstor.org/stable/2691504">A Fibonacci-like sequence of composite numbers</a>, Math. Mag. 63 (1) (1990) 21-25.
%H A083105 J. W. Nicol, <a href="https://doi.org/10.37236/1476">A Fibonacci-like sequence of composite numbers</a>, The Electronic Journal of Combinatorics, Volume 6 (1999), Research Paper #R44.
%H A083105 Carlos Rivera, <a href="http://www.primepuzzles.net/problems/prob_031.htm">Problem 31. Fibonacci- all composites sequence</a>, The Prime Puzzles and Problems Connection.
%H A083105 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,1).
%F A083105 G.f.: (62638280004239857-13174844261034202*x)/(1-x-x^2). [_Colin Barker_, Jun 19 2012]
%p A083105 a:= n-> (<<0|1>, <1|1>>^n. <<62638280004239857, 49463435743205655>>)[1, 1]:
%p A083105 seq(a(n), n=0..20); # _Alois P. Heinz_, Sep 20 2021
%t A083105 LinearRecurrence[{1,1},{62638280004239857,49463435743205655},20] (* _Paolo Xausa_, Nov 07 2023 *)
%Y A083105 Cf. A000032 (Lucas numbers), A000045 (Fibonacci numbers), A083103, A083104, A083216, A082411, A221286.
%K A083105 nonn,easy
%O A083105 0,1
%A A083105 _Harry J. Smith_, Apr 23 2003
%E A083105 Name clarified by _Robert C. Lyons_, Feb 07 2025