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%I #3 Mar 31 2012 10:23:47
%S 3,7,31,211,2311,15017,85091,1616621,22309297,3234846617,200560490131,
%T 3710369067407,20283350901829,872184088778017,307444891294245707,
%U 775932344695001107,961380175077106319537,19548063559901161830551
%N Primes of the form A019565(2^n-1-k)+A019565(k) with minimum k.
%C This sequence can also be defined as: The Primes of the form primorial P(n)/A019565(k)+A019565(k) with minimum k. Conjecture: sequence is defined for any n>=1.
%e for n=1, A019565(2^1-1-0)+A019565(0)=2+1=3 is prime, so a(1)=3;
%e for n=6, A019565(2^6-1-1)+A019565(1)=15015+2=15017 is prime, so a(6)=15017;
%t nmax = 2^2048; npd = 1; n = 1; npd = npd*Prime[n]; While[npd < nmax, tn = 0; tt = 1; cp = npd/tt + tt; While[(IntegerQ[cp]) && (! (PrimeQ[cp])), tn = tn + 1; tt = 1; k1 = tn; o = 1; While[k1 > 0, k2 = Mod[k1, 2]; If[k2 == 1, tt = tt*Prime[o]]; k1 = (k1 - k2)/2; o = o + 1]; cp = npd/tt + tt]; Print[cp]; n = n + 1; npd = npd*Prime[n]]
%Y Cf. A019565, A002110.
%K base,nonn
%O 1,1
%A _Lei Zhou_, Feb 15 2005
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