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.
f[s_List] := Block[{k = 1, p = Times @@ s}, While[ MemberQ[s, k] || !PrimeQ[k*p + 1], k++]; Append[s, k]]; Nest[f, {1}, 69] (* Robert G. Wilson v, Dec 24 2012 *)
v=[1];n=1;while(n<100,s=1+n*prod(i=1,#v,v[i]);if(isprime(s)&&!vecsearch(vecsort(v),n),v=concat(v,n);n=0);n++);v \\ Derek Orr, Jun 16 2015
from gmpy2 import is_prime
from itertools import islice
def agen(startp=1, startset=set()): # generator of terms
aset, p, mink = startset, startp, 1
while True:
an = mink
while an in aset or not is_prime(p*an + 1): an += 1
yield an; aset.add(an); p *= an
while mink in aset: aset.discard(mink); mink += 1
print(list(islice(agen(), 70))) # Michael S. Branicky, May 19 2023
For 1, 3, 5, 7: 1+2 = 3, 1*3+2 = 5, 1*3*5+2 = 17, 1*3*5*7+2 = 107 are primes. - _Daniel Forgues_, Dec 20 2012
f[s_List] := Block[{k = 1, p = Times @@ s}, While[ MemberQ[s, k] || !PrimeQ[k*p + 2], k += 2]; Append[s, k]]; Nest[f, {1}, 62] (* Robert G. Wilson v, Dec 24 2012 *)
3+1 = 4, 3*5+1 = 16, 3*5*6+1 = 91, 3*5*6*8+1 = 721, etc. are nonprimes.
A[1]:= 3: P:= 3:
for n from 2 to 100 do
for k from A[n-1]+1 do
if not isprime(P*k+1) then
A[n]:= k; P:= P*k; break
fi
od od:
seq(A[i],i=1..100); # Robert Israel, Jun 18 2019
seq={3};Do[n=Last[seq]+1;While[PrimeQ[n Times@@seq+1],n++];AppendTo[seq,n];,{100}];seq
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