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.

2, 3, 4, 9, 10, 27, 34, 69, 70, 429, 430, 1059, 1484, 3537, 8284, 65169, 98464, 2061999, 2210564, 10919799, 11521580, 495385137, 567955604, 1112946057, 4926960394, 365847990027

Offset: 1

Author

Rainer Rosenthal and Hugo Pfoertner, Oct 07 2017

Keywords

• nonn
• hard
• more

Examples

			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;
a(7)=34: a(2)+34 = 3+34 = 37, a(4)+34 = 9+34 = 43, a(6)+34 = 27+34 = 61;
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.
		

Crossrefs

Cf. A005115, A103828.

Programs

PARI

PT(x)={print1(x,", ");write("b291163.txt",n++," ",x)};
n=0;
ae=vector(11);
ao=vector(11);
ae[1]=2;PT(ae[1]);
ao[1]=3;PT(ao[1]);
for (m=1,10,\
   start=(ao[m]+1)/2;\
   for (kh=start,100*start,k=kh+kh;\
      for(jj=1,m,j=m-jj+1;if(!isprime(k+ao[j]),next(2)));\
      ae[m+1]=k;PT(k);break(1));\
   start=ae[m+1]/2;\
   for (kh=start,100*start,k=kh+kh+1;\
      for(jj=1,m+1,j=m-jj+2;if(!isprime(k+ae[j]),next(2)));\
      ao[m+1]=k;PT(k);break(1)))
\\ Hugo Pfoertner, Oct 10 2017