cp's OEIS Frontend

A291163 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.

%I A291163 #17 Oct 11 2017 16:17:54
%S A291163 2,3,4,9,10,27,34,69,70,429,430,1059,1484,3537,8284,65169,98464,
%T A291163 2061999,2210564,10919799,11521580,495385137,567955604,1112946057,
%U A291163 4926960394,365847990027
%N A291163 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 A291163 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 A291163 a(7)=34: a(2)+34 = 3+34 = 37, a(4)+34 = 9+34 = 43, a(6)+34 = 27+34 = 61;
%e A291163 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 A291163 (PARI)
%o A291163 PT(x)={print1(x,", ");write("b291163.txt",n++," ",x)};
%o A291163 n=0;
%o A291163 ae=vector(11);
%o A291163 ao=vector(11);
%o A291163 ae[1]=2;PT(ae[1]);
%o A291163 ao[1]=3;PT(ao[1]);
%o A291163 for (m=1,10,\
%o A291163    start=(ao[m]+1)/2;\
%o A291163    for (kh=start,100*start,k=kh+kh;\
%o A291163       for(jj=1,m,j=m-jj+1;if(!isprime(k+ao[j]),next(2)));\
%o A291163       ae[m+1]=k;PT(k);break(1));\
%o A291163    start=ae[m+1]/2;\
%o A291163    for (kh=start,100*start,k=kh+kh+1;\
%o A291163       for(jj=1,m+1,j=m-jj+2;if(!isprime(k+ae[j]),next(2)));\
%o A291163       ao[m+1]=k;PT(k);break(1)))
%o A291163 \\ _Hugo Pfoertner_, Oct 10 2017
%Y A291163 Cf. A005115, A103828.
%K A291163 nonn,hard,more
%O A291163 1,1
%A A291163 _Rainer Rosenthal_ and _Hugo Pfoertner_, Oct 07 2017