%I A100380
%S A100380 1,1,2,1,2,1,4,2,1,2,2,1,3,2,2,1,2,2,1,2,3,2,5,2,1,2,1,3,5,3,2,1,4,1,2,
%T A100380 2,3,2,2,1,3,1,2,1,3,3,2,1,4,2,1,3,2,2,2,1,2,2,1,3,4,2,1,4,3,2,3,1,3,2,
%U A100380 3,2,2,3,2,3,4,3,3,1,4,1,2,5,2,3,2,1,4,4,3,5,3,4,2,4,1,4,2
%N A100380 Least k such that p(n)+p(k)# is prime, where p(i)=i-th prime, p(i)#=i-th 
               primorial.
%C A100380 Conjecture: all prime number can be written as + or - p(n) - or + p(k)#.
%C A100380 The sequence grows remarkably slowly. The largest number occurring within 
               the first 50000 elements is 90. - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), 
               Apr 10 2006
%e A100380 p(8)=19
%e A100380 19+2=21 =3*7
%e A100380 19+6=25 =5*5
%e A100380 19+30=49 =7*7
%e A100380 19+210=229 prime 210=p(4)# so k(8)=4
%t A100380 Table[k := 1;While[Not[PrimeQ[Prime[n]+Product[Prime[i],{i,1,k}]]],k++ 
               ];k,{n,2, 100}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), 
               Apr 10 2006
%Y A100380 Sequence in context: A024559 A061797 A068341 this_sequence A080825 A034693 
               A072342
%Y A100380 Adjacent sequences: A100377 A100378 A100379 this_sequence A100381 A100382 
               A100383
%K A100380 easy,nonn
%O A100380 2,3
%A A100380 Pierre CAMI (pierrecami(AT)tele2.fr), Dec 30 2004
%E A100380 More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), 
               Apr 10 2006