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

%I A261703 #66 Jan 01 2025 18:27:51
%S A261703 139,2,3,5,43,11,7,13,179489311,320377,827,3895650091,151,17,823,191,
%T A261703 8648810893,17548807,83,127,15440491576811767,106961,2143,59,30689,71,
%U A261703 26538557132758528345706017618160870665435147,23,29,11721253,1358804471,5930216438678837,39161,619
%N A261703 Euclid-Mullin sequence (A000945) with initial value a(1) = 139 instead of a(1) = 2.
%C A261703 139 was chosen because of the relatively small initial values a(1), .., a(16).
%H A261703 Tyler Busby, <a href="/A261703/b261703.txt">Table of n, a(n) for n = 1..65</a>
%H A261703 Planetmath.org, <a href="http://planetmath.org/variantsoftheeuclidmullinsequence"> Variants of the Euclid-Mullin sequence</a>
%H A261703 Pollack, Paul; Treviño, Enrique, <a href="http://pollack.uga.edu/mullin.pdf">The Primes that Euclid Forgot.</a>
%t A261703 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 *)
%o A261703 (PARI) spf(n)=factor(n)[1,1]
%o A261703 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;
%Y A261703 Cf. A000945, A000946, A005265, A005266.
%K A261703 nonn
%O A261703 1,1
%A A261703 _Anders Hellström_, Aug 28 2015
%E A261703 a(27)-a(33) from _Jinyuan Wang_, Jul 02 2022
%E A261703 a(34) from _Tyler Busby_, Oct 12 2023