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%I #17 Oct 11 2017 16:17:54
%S 2,3,4,9,10,27,34,69,70,429,430,1059,1484,3537,8284,65169,98464,
%T 2061999,2210564,10919799,11521580,495385137,567955604,1112946057,
%U 4926960394,365847990027
%N a(n) = smallest number k > a(n-1) maximizing the number of primes in all sums a(j)+k, j=1..(n-1), with a(1)=2.
%e a(6)=27 because it is the smallest number producing 3 primes in the sums with all previous terms: a(1)+27 = 2+27 = 29, a(3)+27 = 4+27 = 31, a(5)+27 = 10+27 = 37;
%e a(7)=34: a(2)+34 = 3+34 = 37, a(4)+34 = 9+34 = 43, a(6)+34 = 27+34 = 61;
%e a(8)=69 because it is the smallest number producing 4 primes in the sums with all previous terms: a(1)+69 = 2+69 = 71, a(3)+69 = 4+69 = 73, a(5)+69 = 10+69 = 79, a(7)+69 = 34+69 = 103.
%o (PARI)
%o PT(x)={print1(x,", ");write("b291163.txt",n++," ",x)};
%o n=0;
%o ae=vector(11);
%o ao=vector(11);
%o ae[1]=2;PT(ae[1]);
%o ao[1]=3;PT(ao[1]);
%o for (m=1,10,\
%o start=(ao[m]+1)/2;\
%o for (kh=start,100*start,k=kh+kh;\
%o for(jj=1,m,j=m-jj+1;if(!isprime(k+ao[j]),next(2)));\
%o ae[m+1]=k;PT(k);break(1));\
%o start=ae[m+1]/2;\
%o for (kh=start,100*start,k=kh+kh+1;\
%o for(jj=1,m+1,j=m-jj+2;if(!isprime(k+ae[j]),next(2)));\
%o ao[m+1]=k;PT(k);break(1)))
%o \\ _Hugo Pfoertner_, Oct 10 2017
%Y Cf. A005115, A103828.
%K nonn,hard,more
%O 1,1
%A _Rainer Rosenthal_ and _Hugo Pfoertner_, Oct 07 2017
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