A051315 Euclid-Mullin sequence (A000945) with initial value a(1)=31 instead of a(1)=2.

31, 2, 3, 11, 23, 47059, 7, 5, 89, 19, 2287, 233, 17, 647, 1607, 12637, 103, 13, 163, 4980301, 521, 83, 16561, 540233, 443516695049428313, 109, 37, 1811, 53, 487, 548519020982014152563328120144563684918808813765009178152503015356294212417026402782591

Offset: 1

Author

Labos Elemer

Keywords

• easy
• nonn

Links

• Tyler Busby, Table of n, a(n) for n = 1..37 (terms 1..36 from Robert Price)

Crossrefs

Cf. A000945, A000946, A005265, A005266.

Programs

Maple

spf:= proc(n) local F;
  F:= select(type, map(t -> t[1], ifactors(n,easy)[2]), integer);
   if F <> [] then min(F)
   else min(numtheory:-factorset(n))
   fi
end proc:
a[1]:= 31:
for i from 2 to 31 do
  a[i]:= spf(1 + mul(a[j],j=1..i-1))
od:
seq(a[i],i=1..31); # Robert Israel, Nov 25 2015

Mathematica

a[1]=31; a[n_] := First[ Flatten[ FactorInteger[ 1+Product[ a[ j ], {j, 1, n-1} ] ] ] ]; Array[a, 10]

PARI

gpf(n)=my(f=factor(n)[, 1]); f[#f];
first(m)=my(v=vector(m)); v[1]=31; for(i=2, m, v[i]=gpf(1+prod(j=1, i-1, v[j]))); v \\ Anders Hellström, Nov 25 2015