login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Least k such that (10^k)*(P(n)#) - 1 is prime with P(i)= i-th prime and P(i)#= i-th primorial.
0

%I #9 Aug 06 2014 09:20:24

%S 1,1,2,1,1,1,3,2,1,1,40,1,1,10,10,10,7,17,4,11,15,10,11,54,24,8,11,2,

%T 18,2,6,4,58,3,14,15,1,3,13,16,1,37,4,4,8,11,80,2,37,58,55,34,15,59,

%U 26,1,32,42,47,56,47,4,57,62,27,18,14,17,12,47,19,16,39,9,71,13,6,6,25,10,1,1

%N Least k such that (10^k)*(P(n)#) - 1 is prime with P(i)= i-th prime and P(i)#= i-th primorial.

%e (10^1)*2 -1 = 19 prime so k(1)=1.

%e (10^1)*6 -1 = 59 prime so k(2)=1.

%e (10^2)*30 -1 = 2999 prime so k(3)=2.

%o (PARI) a(n) = {prd = prod(i=1, n, prime(i)); k = 1; while (!isprime(10^k*prd-1), k++); k;} \\ _Michel Marcus_, Aug 06 2014

%Y Cf. A002110.

%K nonn

%O 1,3

%A _Pierre CAMI_, Dec 15 2004

%E Corrected by _Michel Marcus_, Aug 06 2014