A051308 - OEIS

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

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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