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%I #24 Apr 15 2024 07:01:50
%S 0,0,1,3,3,-1,-1,15,31,-1,-65,-1,255,255,-513,-1025,1023,4095,-1,
%T -12289,-8193,32767,49151,-65537,-196609,65535,655359,262143,-1835009,
%U -2097153,4194303,9437183,-6291457,-33554433,-4194305,100663295,83886079,-251658241
%N Partial sums of Berstel sequence (A007420).
%C The subsequence of unique primes begins 3, 31, -12289, -65537. What is the next prime in the sequence?
%C The next prime in the sequence is -113249697660929, followed by 289815643220546158591. - _Harvey P. Dale_, May 15 2016
%H Harvey P. Dale, <a href="/A178885/b178885.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-6,8,-4).
%F a(n) = Sum_{i=0..n} A007420(i) = Sum_{i=0..n} a(n+1) = 2*a(i)-4*a(i-1)+4*a(i-2).
%F G.f.: -x^2*(256*x^11-512*x^10+384*x^9-192*x^8+64*x^7-1) / ((x-1)*(4*x^3-4*x^2+2*x-1)). - _Colin Barker_, Apr 20 2013
%t LinearRecurrence[{3,-6,8,-4},{0,0,1,3},50] (* _Harvey P. Dale_, May 15 2016 *)
%Y Cf. A007420.
%K easy,sign
%O 0,4
%A _Jonathan Vos Post_, Dec 28 2010
%E Corrected by _Harvey P. Dale_, May 15 2016
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