A051326 Euclid-Mullin sequence (A000945) with initial value a(1)=79 instead of a(1)=2.

79, 2, 3, 5, 2371, 7, 39334891, 19, 29397438602292811, 43, 167, 839, 5839, 30402153456526009093473029504929376787635911, 241815479790331, 41, 180922657, 5303, 2389, 13, 31, 11

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Comments

a(23) is a 122-digit prime.

a(5), a(7), a(9), a(14) and a(23) are all the product of the preceding terms + 1. - Robert Price, Jul 10 2015

a(32) requires factoring a composite 292 digit integer. - Robert Price, Sep 05 2021

Links

• Robert Price, Table of n, a(n) for n = 1..31 [corrected Sep 05, 2021]

Crossrefs

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

Programs

Mathematica

a[1]=79; 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]=79; for(i=2, m, v[i]=spf(1+prod(j=1, i-1, v[j]))); v \\ Anders Hellström, Dec 06 2015

Formula

a(n) = A020639(1 + Product_{k=1..n-1} a(k)), a(1) = 79.