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

1,1

Comments

The initial primes 3 and 7 give essentially A000945.

Links

Table of n, a(n) for n=1..39.

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A000945, A000946, A005265, A005266.

Sequence in context: A094683 A094685 A095396 * A257327 A074642 A194034

Adjacent sequences: A051305 A051306 A051307 * A051309 A051310 A051311

Keyword

nonn

Author

Labos Elemer

Extensions

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

Status

approved