This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
n := 1: while true do j := 2: while not isprime(j*n+1) do j := j+1: od: print(j): n := n*j: od:
a[1] = 2; a[n_] := a[n] = Catch[For[an = 2, True, an++, If[PrimeQ[Product[a[k], {k, 1, n - 1}]*an + 1], Throw[an]]]]; Table[a[n], {n, 1, 81}] (* Jean-François Alcover, Nov 27 2012 *)
nxt[{t_,n_}]:=Module[{k=2},While[!PrimeQ[t*k+1],k++];{t*k,k}]; NestList[ nxt,{2,2},80][[All,2]] (* Harvey P. Dale, Oct 03 2020 *)
from gmpy2 import is_prime
from itertools import count, islice
def agen(): # generator of terms
p = 1
while True:
an = next(k for k in count(2) if (t:=p*k+1) == 1 or is_prime(t))
p *= an
yield an
print(list(islice(agen(), 81))) # Michael S. Branicky, Jan 20 2024
a[1] = 1; a[n_] := a[n] = Catch[For[k = 2, True, k++, an = k*a[n - 1]; If[PrimeQ[an + 1], Throw[an]]]]; Table[a[n], {n, 1, 23}] (* Jean-François Alcover, Nov 27 2012 *)
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