A265009 a(1)=3; for n>1, if n is odd a(n) = spf(Product_{k=1..n-1}(a(k))+1) else a(n) = spf(Product_{k=1..n-1}(a(k))-1), where spf is "smallest prime factor".

3, 2, 7, 41, 1723, 5, 14835031, 220078129935929, 241, 23, 79, 101, 23291, 11, 223, 122386298896281959929015788890561251765109069, 38803, 17, 8209, 59, 199, 3340389589, 11527, 13, 47939, 1163, 599, 27198087874669514440553, 181936481, 31, 383, 9623, 739, 33287, 1061, 6493520653, 587, 709, 6548057, 1823, 361789, 20183

Offset: 1

Author

Anders Hellström, Nov 30 2015

Keywords

• nonn

Crossrefs

Cf. A000945, A005265.

Programs

Mathematica

a[1] = 3; a[n_] := a[n] = FactorInteger[ Product[a[k], {k, n - 1}] + If[OddQ@ n, 1, -1]][[1, 1]]; Array[a, {16}] (* Michael De Vlieger, Nov 30 2015 *)

PARI

spf(n)=my(f=factor(n)[1, 1]); f
first(m)=my(v=vector(m)); v[1]=3; for(i=2, m,;v[i]=spf((-1)^(i+1)+prod(j=1, i-1, v[j]))); v

Extensions

a(20)-a(42) from Hans Havermann, Dec 06 2015