A036013 a(n) = smallest number > 1 such that a(1)a(2)...a(n) - 1 is prime (or 1).

2, 2, 2, 3, 2, 4, 2, 3, 6, 4, 5, 5, 5, 10, 4, 3, 5, 8, 22, 13, 14, 2, 5, 5, 2, 20, 9, 9, 24, 5, 26, 15, 14, 25, 25, 4, 9, 30, 9, 21, 12, 11, 10, 2, 40, 19, 8, 13, 11, 50, 3, 25, 25, 8, 5, 25, 46, 19, 47, 54, 9, 13, 14, 43, 4, 24, 28, 16, 33, 25, 152, 2, 11, 22, 6, 78, 87, 7, 10, 21

Offset: 1

Author

Russell Easterly

Keywords

• nonn
• nice
• easy

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..1600 (terms 1..300 from T. D. Noe)

Crossrefs

Cf. A036012, A058000 (corresponding primes).

Programs

Mathematica

sng1[{t_,a_}]:=Module[{k=2},While[CompositeQ[t k-1],k++];{t*k,k}]; NestList[sng1,{2,2},80][[;;,2]] (* Harvey P. Dale, May 20 2023 *)

Python

from sympy import isprime
from itertools import count
a,p = [2],2
for _ in range(100):
    q = next(filter(lambda x:isprime(x*p-1), count(2)))
    p = p*q
    a.append(q)
print(a) # Nicholas Stefan Georgescu, Mar 06 2023

Extensions

More terms from Erich Friedman. More terms from Jud McCranie, Jan 26 2000.