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%I #6 Oct 12 2013 15:14:06
%S 3,2,1,1,1,1,2,1,3,5,2,4,6,3,5,7,26,5,7,11,10,1,1,1,11,5,3,8,3,20,14,
%T 4,2,39,1,16,4,6,3,56,8,7,17,14,4,21,7,13,13,22,30,10,22,6,2,43,3,17,
%U 26,21,32,10,28,30,15,28,22,74,23,33,11,8,1,4,3,5,2,29,3,68,36,14,1,133,4
%N Least k such that k*p(n)#-p(n+1) is prime, where p(i)# denotes the i-th primorial and p(i) denotes the i-th prime.
%C k*p(n)#-p(n+1) is the greatest prime < k*p(n)#-p(n+1)-1 and if k*p(n)#-p(n+1)-1 is not prime it is the greatest prime < k*p(n)#-p(n+1) P is given in one other sequence
%e 1*2*3*5*7*11*13-17=30013, 1*p(6)#-p(7)=30013, 1 is the least k for n=6
%e 30013 is prime
%e a(7)=2 since 2*17#-19 = 1021001 is prime.
%o (PARI) primorial(n) = prod(i=1,primepi(n),prime(i)) A090189(n) = {local(k,a,b);k=1;a=primorial(prime(n));b=prime(n+1);while(!isprime(a*k-b),k++);k}
%K base,nonn
%O 1,1
%A _Pierre CAMI_, Jan 21 2004
%E a(7) corrected by _Michael B. Porter_, Jan 29 2010