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

1,1

Comments

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

Links

Table of n, a(n) for n=1..34.

Planetmath.org, Variants of the Euclid-Mullin sequence

Pollack, Paul; Treviño, Enrique, The Primes that Euclid Forgot.

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 *)

Prog

(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;

Crossrefs

Cf. A000945, A000946, A005265, A005266.

Sequence in context: A223192 A199839 A005447 * A266003 A340800 A333135

Adjacent sequences: A261700 A261701 A261702 * A261704 A261705 A261706

Keyword

nonn

Author

Anders Hellström, Aug 28 2015

Extensions

More terms from Jinyuan Wang, Jul 02 2022

a(34) from Tyler Busby, Oct 12 2023

Status

approved