A051319 Euclid-Mullin sequence (A000945) with initial value a(1)=47 instead of a(1)=2.

47, 2, 5, 3, 17, 23971, 7, 4022094091, 3673, 11, 32915297, 21513736430048030802333949693291, 43, 349, 613, 37, 6767927, 59, 71249, 19, 4455467, 997, 181, 593, 681271, 113, 13, 1205224649, 1699, 533327, 1361, 29

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Links

• Tyler Busby, Table of n, a(n) for n = 1..35
• Andrew R. Booker and Sean A. Irvine, The Euclid-Mullin graph, arXiv preprint arXiv:1508.03039 [math.NT], 2015-2016.

Crossrefs

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

Programs

Mathematica

a[1]=47; a[n_] := First[ Flatten[ FactorInteger[ 1+Product[ a[ j ], {j, 1, n-1} ] ] ] ]; Array[a, 10]

PARI

spf(n)=factor(n)[1, 1]; \\ A020639
first(m)=my(v=vector(m)); v[1]=47; for(i=2, m, v[i]=spf(1+prod(j=1, i-1, v[j]))); v \\ Anders Hellström, Nov 25 2015; corrected by Michel Marcus, Oct 10 2023