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%I #40 Sep 20 2021 09:24:56
%S 1786772701928802632268715130455793,
%T 1059683225053915111058165141686995,
%U 2846455926982717743326880272142788,3906139152036632854385045413829783,6752595079019350597711925685972571,10658734231055983452096971099802354
%N Second-order linear recurrence sequence with a(n) = a(n-1) + a(n-2).
%C a(0) = 1786772701928802632268715130455793, a(1) = 1059683225053915111058165141686995. This is the second-order linear recurrence sequence with a(0) and a(1) coprime that R. L. Graham in 1964 stated did not contain any primes. It has not been verified. Graham made a mistake in the calculation that was corrected by D. E. Knuth in 1990.
%D P. Ribenboim, The Little Book of Big Primes. Springer-Verlag, 1991, p. 178.
%H Indranil Ghosh, <a href="/A083103/b083103.txt">Table of n, a(n) for n = 0..4617</a>
%H 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 D. Ismailescu, 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 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H 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 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 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,1).
%F G.f.: (1786772701928802632268715130455793-727089476874887521210549988768798*x)/(1-x-x^2). [_Colin Barker_, Jun 19 2012]
%t LinearRecurrence[{1,1},{1786772701928802632268715130455793, 1059683225053915111058165141686995},70] (* _Harvey P. Dale_, Oct 17 2011 *)
%Y Cf. A000032 (Lucas numbers), A000045 (Fibonacci numbers), A083104, A083105.
%K nonn,easy
%O 0,1
%A _Harry J. Smith_, Apr 22 2003
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