A090189 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.

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, 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, 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

Offset: 1

Author

Pierre CAMI, Jan 21 2004

Keywords

• base
• nonn

Comments

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

Examples

			1*2*3*5*7*11*13-17=30013, 1*p(6)#-p(7)=30013, 1 is the least k for n=6
30013 is prime
a(7)=2 since 2*17#-19 = 1021001 is prime.
		

Programs

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}

Extensions

a(7) corrected by Michael B. Porter, Jan 29 2010