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%I #10 Jun 10 2017 12:19:05
%S 7167305,20224749,32848229,63138028,98444311,361075686,530778019,
%T 541985251,562407560,608779540,678479762,700368011,816865538
%N Numbers k such that p1 = prime(k) + prime(k+1) + prime(k+2), p2 = p1 + prime(k+3) + prime(k+4), p3 = p2 + prime(k+5) + prime(k+6), p4 = p3 + prime(k+7) + prime(k+8), p5 = p4 + prime(k+9) + prime(k+10), p6 = p5 + prime(k+11) + prime(k+12), p7 = p6 + prime(k+13) + prime(k+14) and p8 = p7 + prime(k+15) + prime(k+16) are all prime
%C a(12)=700368011: p9 = p8 + prime(k+17) + prime(k+18) =
%C 298451681831 prime - first such case. - _Zak Seidov_, Jun 10 2017
%o (PARI) list(lim)=my(v=List(), u=primes(17), n=1, p1, p3, p4, p5, p6, p7); forprime(s=u[7]+1, , if(n++>lim, break); u=concat(u[2..17], s); if(isprime(p1=u[1]+u[2]+u[3]) && isprime(p2=p1+u[4]+u[5]) && isprime(p3=p2+u[6]+u[7]) && isprime(p4=p3+u[8]+u[9]) && isprime(p5=p4+u[10]+u[11]) && isprime(p6=p5+u[12]+u[13]) && isprime(p7=p6+u[14]+u[15]) && isprime(p7+u[16]+u[17]), listput(v, n))); Vec(v) \\ _Charles R Greathouse IV_, Jun 10 2017
%Y Subsequence of A288107.
%K nonn,more
%O 1,1
%A _Zak Seidov_, Jun 09 2017
%E a(6)-a(13) from _Charles R Greathouse IV_, Jun 10 2017
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