A051308 Euclid-Mullin sequence (A000945) with initial value a(1)=5 instead of a(1)=2.

5, 2, 11, 3, 331, 19, 199, 53, 21888927391, 29833, 101, 71, 23, 311, 7, 72353, 13, 227, 96014559769, 5641, 41, 82107739003, 67, 169637539, 61, 29, 31319, 17, 97, 238591921, 313, 102065429, 157, 37, 595553520313, 244217, 241, 4773229353714971081083834237, 103

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Comments

The initial primes 3 and 7 give essentially A000945.

Examples

			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.
		

Crossrefs

Cf. A000945, A000946, A005265, A005266.

Programs

Mathematica

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

PARI

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

Extensions

a(38)-a(39) from Robert Price, Jul 19 2015