A051315 - OEIS

%I #23 Oct 07 2023 21:38:02

%S 31,2,3,11,23,47059,7,5,89,19,2287,233,17,647,1607,12637,103,13,163,

%T 4980301,521,83,16561,540233,443516695049428313,109,37,1811,53,487,

%U 548519020982014152563328120144563684918808813765009178152503015356294212417026402782591

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

%H Tyler Busby, <a href="/A051315/b051315.txt">Table of n, a(n) for n = 1..37</a> (terms 1..36 from Robert Price)

%p spf:= proc(n) local F;

%p   F:= select(type, map(t -> t[1], ifactors(n,easy)[2]), integer);

%p    if F <> [] then min(F)

%p    else min(numtheory:-factorset(n))

%p    fi

%p end proc:

%p a[1]:= 31:

%p for i from 2 to 31 do

%p   a[i]:= spf(1 + mul(a[j],j=1..i-1))

%p od:

%p seq(a[i],i=1..31); # _Robert Israel_, Nov 25 2015

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

%o (PARI) gpf(n)=my(f=factor(n)[, 1]); f[#f];

%o 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

%Y Cf. A000945, A000946, A005265, A005266.

%K easy,nonn

%O 1,1

%A _Labos Elemer_