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A289111 a(n) = (2^49 - 2)*n/3 + 444813635231.

%I A289111 #17 Sep 08 2022 08:46:19
%S A289111 444813635231,188094798109001,375744782582771,563394767056541,
%T A289111 751044751530311,938694736004081,1126344720477851,1313994704951621,
%U A289111 1501644689425391,1689294673899161,1876944658372931,2064594642846701,2252244627320471,2439894611794241
%N A289111 a(n) = (2^49 - 2)*n/3 + 444813635231.
%C A289111 For all n, the numbers a(n) and a(n) + 2 form a pair of consecutive Riesel numbers.
%C A289111 Conjecture: a(0) + 1 = 444813635232 is the smallest nonnegative even number m such that for all k >= 1 the absolute values of the numbers m - 2^k + 1 and m - 2^k - 1 are composite.
%H A289111 Colin Barker, <a href="/A289111/b289111.txt">Table of n, a(n) for n = 0..1000</a>
%H A289111 Carlos Rivera, <a href="http://primepuzzles.net/coll20th/coll20th-019.htm">Collection 20th - 019</a>
%H A289111 Wikipedia, <a href="https://en.wikipedia.org/wiki/Riesel_number">Riesel number</a>
%H A289111 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A289111 a(n) = (2^49 - 2)*n/3 + 444813635231.
%F A289111 G.f.: (444813635231 + 187205170838539*x)/(1 - x)^2.
%F A289111 From _Colin Barker_, Jun 25 2017: (Start)
%F A289111 a(n) = 7*(63544805033 + 26807140639110*n).
%F A289111 a(n) = 2*a(n-1) - a(n-2) for n>1.
%F A289111 (End)
%p A289111 seq(coeff(series((444813635231+187205170838539*x)/(1-x)^2,x,n+1), x, n), n = 0 .. 15); # _Muniru A Asiru_, Oct 01 2018
%t A289111 Table[(2^49 - 2) n/3 + 444813635231, {n, 0, 13}] (* or *)
%t A289111 CoefficientList[Series[(444813635231 + 187205170838539 x)/(1 - x)^2, {x, 0, 13}], x]
%o A289111 (Magma) [(2^49-2)*n/3+444813635231: n in [0..13]];
%o A289111 (PARI) a(n)=(2^49-2)*n/3+444813635231
%o A289111 (PARI) Vec(7*(63544805033 + 26743595834077*x) / (1 - x)^2 + O(x^15)) \\ _Colin Barker_, Jun 25 2017
%o A289111 (GAP) List([0..15],n->(2^49-2)*n/3+444813635231); # _Muniru A Asiru_, Oct 01 2018
%Y A289111 Cf. A101036.
%K A289111 nonn,easy
%O A289111 0,1
%A A289111 _Arkadiusz Wesolowski_, Jun 24 2017