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%I #18 Sep 08 2022 08:46:19
%S 247371098957,187897355572727,375547340046497,563197324520267,
%T 750847308994037,938497293467807,1126147277941577,1313797262415347,
%U 1501447246889117,1689097231362887,1876747215836657,2064397200310427,2252047184784197,2439697169257967
%N a(n) = (2^49 - 2)*n/3 + 247371098957.
%C For all n, the numbers a(n) and a(n) + 2 form a pair of consecutive Sierpiński numbers.
%C Conjecture: a(0) + 1 = 247371098958 is the smallest nonnegative even number m such that for all k >= 1 the numbers m + 2^k + 1 and m + 2^k - 1 are composite.
%H Muniru A Asiru, <a href="/A288477/b288477.txt">Table of n, a(n) for n = 0..5000</a>
%H Carlos Rivera, <a href="http://primepuzzles.net/coll20th/coll20th-019.htm">Collection 20th - 019</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Sierpinski_number">Sierpinski number</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F G.f.: (247371098957 + 187402613374813*x)/(1 - x)^2.
%p seq(coeff(series((247371098957+187402613374813*x)/(1-x)^2,x,n+1), x, n), n = 0 .. 15); # _Muniru A Asiru_, Oct 01 2018
%t Table[(2^49 - 2) n/3 + 247371098957, {n, 0, 13}] (* or *)
%t CoefficientList[Series[(247371098957 + 187402613374813 x)/(1 - x)^2, {x, 0, 13}], x] (* _Michael De Vlieger_, Jun 09 2017 *)
%o (Magma) [(2^49-2)*n/3+247371098957: n in [0..13]];
%o (PARI) a(n)=(2^49-2)*n/3+247371098957
%o (GAP) List([0..15],n->(2^49-2)*n/3+247371098957); # _Muniru A Asiru_, Oct 01 2018
%Y Cf. A076336.
%K nonn,easy
%O 0,1
%A _Arkadiusz Wesolowski_, Jun 09 2017
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