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A243196 Number of primorial numbers < 10^n. 0

%I #12 Jun 02 2014 22:14:29

%S 3,4,5,6,7,8,9,9,10,11,11,12,13,13,14,14,15,16,16,17,17,18,18,19,20,

%T 20,21,21,22,22,23,23,24,24,25,25,26,26,27,27,28,28,29,29,30,30,31,31,

%U 32,32,33,33,34,34,34,35,35,36,36,37,37,38,38,39,39,40,40,40,41,41,42,42,43

%N Number of primorial numbers < 10^n.

%e There are 5 primorial numbers < 10^3: 1, 2, 6, 30 and 210. Thus a(3) = 5.

%o (PARI) hashp(n)=prod(i=1,n,prime(i))

%o a(n)={tot=1;for(k=1,10^n,if(hashp(k)<10^n,tot++);if(hashp(k)>10^n,break));return(tot)}

%o n=1;while(n<100,print1(a(n),", ");n++)

%o (PARI) {a(n) = my(p=1, m=10^n); for(k=1, n+3, if(m <= (p *= prime(k)), return(k)))}; /* _Michael Somos_, Jun 02 2014 */

%Y Cf. A002110.

%K nonn

%O 1,1

%A _Derek Orr_, Jun 01 2014

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