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%I #32 Mar 03 2023 16:26:49
%S 33647,100943,302831,908495,2725487,8176463,24529391,73588175,
%T 220764527,662293583,1986880751,5960642255,17881926767,53645780303,
%U 160937340911,482812022735,1448436068207,4345308204623,13035924613871,39107773841615,117323321524847,351969964574543
%N a(n) = 33648*3^n - 1.
%C For n > 0, this is the trajectory of 100943 under the map x -> 3*x+2.
%C 100943 is the least starting value > 0 where the trajectory under the map in the previous comment does not reach a prime after a small number of steps.
%C Are there any primes > 100943 in the sequence (cf. A354747 and A354748)?
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3).
%F G.f.: (33647 - 33645*x)/((1 - x)*(1 - 3*x)). - _Stefano Spezia_, Jun 21 2022
%t 33648*3^Range[0,30]-1 (* or *) LinearRecurrence[{4,-3},{33647,100943},30] (* _Harvey P. Dale_, Mar 03 2023 *)
%o (PARI) a(n) = 33648*3^n-1
%o (Python)
%o a = [33647]; [a.append(3*a[-1]+2) for n in range(21)]
%o print(a) # _Michael S. Branicky_, Jun 20 2022
%Y Cf. A016789, A052333, A354747, A354748.
%K nonn,easy
%O 0,1
%A _Felix Fröhlich_, Jun 20 2022