A261703 Euclid-Mullin sequence (A000945) with initial value a(1) = 139 instead of a(1) = 2.

139, 2, 3, 5, 43, 11, 7, 13, 179489311, 320377, 827, 3895650091, 151, 17, 823, 191, 8648810893, 17548807, 83, 127, 15440491576811767, 106961, 2143, 59, 30689, 71, 26538557132758528345706017618160870665435147, 23, 29, 11721253, 1358804471, 5930216438678837, 39161, 619

Offset: 1

Author

Anders Hellström, Aug 28 2015

Keywords

• nonn

Comments

139 was chosen because of the relatively small initial values a(1), .., a(16).

Links

• Tyler Busby, Table of n, a(n) for n = 1..65
• Planetmath.org, Variants of the Euclid-Mullin sequence
• Pollack, Paul; Treviño, Enrique, The Primes that Euclid Forgot.

Crossrefs

Cf. A000945, A000946, A005265, A005266.

Programs

Mathematica

f[1] = 139; f[n_] := f[n] = FactorInteger[Product[f[i], {i, 1, n - 1}] + 1][[1, 1]] ; Table[f[n], {n, 1, 20}] (* Michael De Vlieger, Aug 28 2015, after program at A000945 *)

PARI

spf(n)=factor(n)[1,1]
first(m)=my(v=vector(m));v[1]=139;print1(v[1],", ");for(i=2,m,v[i]=spf(1+prod(k=1,i-1,v[k]));;print1(v[i],", "));v;

Extensions

a(27)-a(33) from Jinyuan Wang, Jul 02 2022

a(34) from Tyler Busby, Oct 12 2023