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Euclid-Mullin sequence (A000945) with initial value a(1)=5 instead of a(1)=2.
39

%I #20 Aug 17 2015 03:30:49

%S 5,2,11,3,331,19,199,53,21888927391,29833,101,71,23,311,7,72353,13,

%T 227,96014559769,5641,41,82107739003,67,169637539,61,29,31319,17,97,

%U 238591921,313,102065429,157,37,595553520313,244217,241,4773229353714971081083834237,103

%N Euclid-Mullin sequence (A000945) with initial value a(1)=5 instead of a(1)=2.

%C The initial primes 3 and 7 give essentially A000945.

%e 5*2*11*3 + 1 = 331, which is prime; the least prime factor of 330*331 + 1 = 109231 = 19*5749 is 19, so a(6) = 19.

%t a[1]=5; a[n_] := First[ Flatten[ FactorInteger[ 1+Product[ a[ j ], {j, 1, n-1} ] ] ] ]; Array[a, 10]

%o (PARI) spf(n)=my(f=factor(n)[1,1]);f;

%o first(m)=my(v=vector(m));v[1]=5;for(i=2,m,v[i]=spf(1+prod(j=1,i-1,v[j])));v; \\ _Anders Hellström_, Aug 15 2015

%Y Cf. A000945, A000946, A005265, A005266.

%K nonn

%O 1,1

%A _Labos Elemer_

%E a(38)-a(39) from _Robert Price_, Jul 19 2015