A051316 Euclid-Mullin sequence (A000945) with initial value a(1)=37 instead of a(1)=2.

37, 2, 3, 223, 31, 7, 127, 5, 11, 17, 157, 390191, 23339, 29, 283, 73, 19, 47, 381735266856929, 149, 83, 71, 311, 9791, 4007, 3101629, 207541, 2591, 13, 2414519329, 107, 41, 53

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Comments

a(34) is a 95-digit prime.

Links

• Tyler Busby, Table of n, a(n) for n = 1..42 (terms 1..39 from Robert Price)

Crossrefs

Cf. A000945, A000946, A005265, A005266, A020639.

Programs

Mathematica

a[1]=37; a[n_] := First[ Flatten[ FactorInteger[ 1+Product[ a[ j ], {j, n-1} ] ] ] ]; Array[a, 15]

PARI

spf(n)=my(f=factor(n)[1, 1]); f; \\ A020639
first(m)=my(v=vector(m)); v[1]=37; for(i=2, m, v[i]=spf(1+prod(j=1, i-1, v[j]))); v \\ Anders Hellström, Nov 26 2015

Formula

a(n) = A020639(1 + Product_{k=1..n-1} a(k)), a(1) = 37.